Class 12 - Mathematics 2026 Guess Paper (Chapter 4 Concepts with Examples) - Punjab Board

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[00:00:00]Assalam Walekum students. This is Teacher Tauba Here Signing in From the YouTube Most Trusted Platform TBT Tutorials by Tauba.

[00:00:08]On your demand, you have told me in the comment section that this example of chapter number four, different parts of which are coming, is most important and I have also explained this to you in my entire test series that this example is very important. For this I am going to tell you in this video.

[00:00:22]And by doing all these parts, your MCQs, shorts and long concepts will become clear to a great extent.

[00:00:28]And children, you will be able to fully attempt the questions of this chapter number four on the basis of your creativity in the paper.

[00:00:36]Ok? Now this example of mine, son, is example number nine for you. Ok? And this is coming between your 4.2 and 4.3.

[00:00:42]Ok? Now you can also take screenshots from here. Ok?

[00:00:45]Look at this in your book, look at your text book, it starts from here and ends here. He has solved it in a very simple way.

[00:00:50]Whereas this is a proper way to explain how to solve it.

[00:00:54]So now let me tell you guys that this video is going to be very informative for you.

[00:00:58]And if you get even a little information from this and it is useful to you, then please go and subscribe to the channel and press the bell icon for all and share this video of yours and make it reach a large community. Ok? Come on kids, let's start now.

[00:01:13]Bismillah Rahmanirrahim. Rabbi Jidni Ilma Sallallahu Alaihi Wasallam.

[00:01:19]Ok? Come on sir. Bismillah Rahman Rahim.

[00:01:21]Example number nine chapter number four. First of all, I told you in the video that I made last night that you have to memorize slope intercept form by heart. So I am repeating this again.

[00:01:30]1 2 3 4 5 6 are coming to us.

[00:01:33]Ok? Look, we are getting a total of six till here. And in this, first of all what comes to us is the slope intercept form y = mx + c, after that the two intercept form which comes to us is x a + y b = 1, son, you have to memorize this completely.

[00:01:48]Ok? These will come in your MCQs as to which ones these are. After that, see here the normal form which is coming is equal to x cos apha + y sin apha = p. and point slope form equal to y - y1 = m x - x1.

[00:02:00]Ok? After that, the number fifth that is coming is two point slope form.

[00:02:04]y - y1 = y2 - y1 is multiplying x2 - x1 or your x - x1 on the side. Ok? In symmetric form your x - x1 over cos apha = y - y1 sin apha = 1 You have to memorize all these things for MCQs because these will come there for proper recognition and identification.

[00:02:23]Ok? That is, they would have written it in such a way that two slope form two point slope form is, the options would have been given below. You have to tick that. Now look at this concept with example, I am explaining this entire concept to you through examples. Now look at this example which is coming in your book.

[00:02:36]Look, this is total six, that means he has given you the equation.

[00:02:39]Transform the equation 5x - 12y + 39 = 0 into all its forms. You have to create this one equation. Ok? So, all six parts of this chapter will cover a lot of weightage and the concepts will also become clear to you all, Insha Allah. Ok? Ok? Now look at transform the equation here it is.

[00:02:56]First of all you have to take it to slope intercept form at number one. I told you earlier that the slope intercept form which is coming is y = mx + c, what we have is the equation of a straight line. Ok? This is what you have in the slope intercept form.

[00:03:06]Now you wrote this equation here.

[00:03:08]y 5x - 12y + 39 = 0 First thing you do is halve y. So since y was negative here, I moved y over there.

[00:03:16]I left all the other things lying here.

[00:03:18]So -12y there becomes +12y, kids. So I can write this straight also. It does n't matter that it's on the right hand side here.

[00:03:25]This is the left hand side here. And when I'm writing this by making a little arrow and correcting it, I brought 12y here. I have brought it here.

[00:03:30]And by doing this I will not change its sign.

[00:03:32]I am just changing his arrangements, children. Ok?

[00:03:36]What should I do now? Here 12 is being multiplied by this.

[00:03:38]So 12 will go down and divide.

[00:03:39]So, y = 5x over 12 + 3912. It has come to you.

[00:03:44]Below this when you have made this.

[00:03:45]After this you don't have to do anything else.

[00:03:47]You have to directly write this standard form.

[00:03:48]y = mx + c When you write this, now you can arrange both of them like this, I have done this to explain it to you.

[00:03:55]You have to compare these two. Look, I have written by comparing m equal to how much is coming to us here? This is x. This is x. So 512 is coming in place of m.

[00:04:02]So the value of m you have come to is 512.

[00:04:05]Look at this and if we look at the value of c from here, it is coming out to be 39/12. Ok? Now yours is complete. What is this first one of yours? Your slope intercept form. This is your complete answer.

[00:04:15]Son, in this you will also get short answers of two marks and you will also get one question in MCQs. Ok? It is possible that whatever is there in the form of long may come as a part, Allah Taala knows it better.

[00:04:25]Inshallah it will be easy. Ok? Now I will write this equation again.

[00:04:29]Look here, this is written in front of you and what am I going to change it to?

[00:04:32]Because the second part of mine is telling me to change this to two intercept form.

[00:04:36]Look, look in the book. So you have to write the two intercept forms here, my children. My students, look, you have written x a + y b = 1. Now you have written this equation again here and after writing it, what you have to do is children, look, the constant term that is coming is the x term. This is the y term. This is our straight line equation with two variables.

[00:04:53]Because the power of all these variables is one.

[00:04:56]You can't see two powers anywhere, right? The 5x key is nowhere to be seen. So what do you have to do? 39 has to be moved to that side of the equation.

[00:05:02]When we take it there, it will become -39. Because he was +39 here.

[00:05:06]What do you want to do now, children? Why divide the whole equation by -39? Because I had told you this last night also, I had told you this in the video that this one which is coming, you have to make it total one on the right hand side.

[00:05:17]Whatever is constant here, divide it by itself and bring one here.

[00:05:20]So here we are getting -39, so by what should I divide the entire equation, son? I'm going to divide this total by -39.

[00:05:26]So here also the sign of 5x over -39 minus came as it is. 12y over -39 = -39 -39 This is written as 9. Cut it out and rewrite it. -39 -39 Now this will be cut from -39 -39. The forest will come. But what will happen here? Look, 5x over -39, now this minus and minus will become plus.

[00:05:48]Because this is also a sign, this sign will be multiplied by that sign. Two signs cannot exist together in such a way that there is something above and something else below the fraction and you have to solve it properly.

[00:05:56]So you have to go there and multiply it. It will be a plus. And this is how your format came into existence. Now you see, in this equation, first of all your x is sitting alone, so what is this variable here doing with x? x is a variable, we don't need this coefficient. We need a single x up in the numerator and we need a single y in the children. So go down and divide five. Because five was being multiplied upwards. So if one thing is being multiplied at the top in any equation i.e. any fraction, then it will be divided at the bottom. So this means that going below -39, that fraction will become one and it will go into division. - 395 Same case will happen with 12 also. 12 What will happen below? Divide will go below 39 and it will come like this. Ok? Now son, what has happened here? That's how you made this equation. Now you have to immediately bring this standard form that is coming to you and write it here. When you write here, now you can compare it.

[00:06:43]Okay kids? Look at this. Now you wrote this here. Now I am going to compare.

[00:06:46]x is in place of x. Absolutely fine. Instead of y, it is y. Absolutely correct. Now what is coming in place of a? -39 5 So a = -39/5.

[00:06:54]And what is the value of b coming out? 39 and 12, so these are your two calculated values ​​of a and b. Is it okay son? It has come here.

[00:07:01]And now look at this, 5x - 12 + 39, after doing this till here, your entire work is complete. What have you taken out of it? Two intercept form is taken out comfortably that it will come like this. Ok? And I have written this here only for comparison.

[00:07:14]Ok? What's coming next?

[00:07:17]Look son, now after doing this till here, you have written it like this for comparison and for your convenience. Ok? Otherwise your answer was complete till here. It would be good if you try it like this. The concept will be clear. Everything will become absolutely strong.

[00:07:27]Now number three form is coming to us, normal form. So look, I rewrote this equation which was the only one given to me. Now I will change it to normal form. So I should write the normal form equation immediately. Here x cos alpha + y sin apha = p is coming in normal form. Now you have written this equation here. Ok? Write it down here. We will do this step wise from step number one because now the procedure is getting a little longer.

[00:07:47]Those first two were very easy.

[00:07:49]Write in the form, how do we write this? ax is the first step, see this equation is already written as ax + by + c = 0, this is your equation of straight line with two variables, in this two variables are coming x and y but see the power of all is one, so this is a straight line equation but with two variables. So what did you do?

[00:08:08]5x - 12y + 39 Look at this, it is written like this.

[00:08:11]Both these things are written the same.

[00:08:12]This is ax. This is your axe. This is by. This is by. Don't get confused about your sign. The signs of that number come in it.

[00:08:19]Understand that you will come into his custody. They come into his property. Ok? So this equation was already in this form for you.

[00:08:24]What do you have to do now? This has to be compared. a what's coming is your five coming. Look, compare these two.

[00:08:28]This a is five and the b that is coming out is -12. I just told you [sound of clearing throat] that whatever sign there is, it's denoting that coefficient.

[00:08:36]And the c that is coming 39 s look c 39 s come.

[00:08:41]You have written down these values. What are we going to do now, kids? See here. Now the second step is coming.

[00:08:45]What do you have to do in the second step? You have to calculate a² + b² under root i.e. magnitude.

[00:08:48]So where a = 5 we have and b = what we are getting is -12. Okay kids?

[00:08:54]What will happen now sir? Now put the value here. Here comes the square plus of 5. The whole square of -12 and the square of the whole under root of 5 is 25 and -12 is going to be multiplied with -12 and the result is 144. An under route came over it.

[00:09:07]When you enter 25 + 144. 169. 169 on the calculator, you will know it very well that it is a perfect square and the answer will be 13. Ok? So whose value have you found? This is the value you have received. Now divide the whole equation by 13.

[00:09:21]What do you want to do with this value that has come to you? The entire equation which is your original equation. So, I'll write it again here. 5x - 12y + 39 = 0 We have to divide this by 13.

[00:09:32]So look at this I did it from 13. This was also done from 13. 39 was also converted into 13. = 0 Now you can cut and shoot the things that are being cut. You can always reduce it. So 5 13x - 12 13y + 13 * 1 = 13 13 * 3 = 39 So here comes three. Ok?

[00:09:47]You guys should not get confused about this. Now what will be step number four? Make the constant term negative. Now look at the constant term that is coming, this constant term is coming in this equation that you have got.

[00:09:56]You have to make it negative. Why make it negative? Because the value of son p is greater than zero. Whatever your p is coming here. Look, understand the matter. There is no rote learning in this. Look at this yourself, you have to make this equation at the end.

[00:10:07]So look what is the p coming here? Here p is coming out positive. That is, the value of p is greater than zero. is a value greater than zero.

[00:10:12]So how do you create value greater than zero? When something negative happens here, what will happen here? It will be negative here.

[00:10:19]So if I take it to that side of the equation, it will become a plus there.

[00:10:22]Because on which side is she already sitting? It is sitting on the left hand side and it is positive. Ok? So what will I do with this? Multiply. To make this negative, I'll multiply the entire equation by -1.

[00:10:30]So when I look at the whole equation, I can't do just this.

[00:10:33]I told you earlier that justice has to be done equally in maths. So -5 51 becomes 13x. Then what will happen here?

[00:10:40]Instead of minus, it will become plus. The sign will change.

[00:10:42]121 13y and what will happen to this plus that is coming? It will become -3. Is it okay son? What have I done? i did not do anything.

[00:10:47]I just looked at this entire equation, this is what is written, for this multiply the equation by -1. That means I have multiplied this equation by -1.

[00:10:56]Ok? Now see for yourself what will happen if you multiply it by -1? This is -5/13 and what will this become? Minus minus + 121 13y And what will this become? Minus plus - 3 = 0 What should I do now son? I have to bring it back in the same form. So I will kick -5/1 13x + 121 13y = 3 over there and say go son, go over there. I made you negative here.

[00:11:15]Now go there and be positive. Now what will happen if he goes there? It will become positive. Now look, you have this equation, after this you don't have to do anything else.

[00:11:24]That means four steps have been completed. I have come this far. The whole thing is over. Now immediately write your equation in standard form. equal to x cos apha + y sin apha = p. Now compare these two.

[00:11:34]Ok? Now what will you do in comparison? Look carefully at the place of x and the place of cos alpha is -5/13. So cos apha = -5/13 and here y is in place of y. Son, I will discontinue a little.

[00:11:46]Fajr Azaan is being called. Ok?

[00:11:48]So I come to you again. Yes son, welcome back.

[00:11:53]Recite Darood Sharif once again. Sallallahu Alaihi Wasallam and recite the prayer. Rabbi Zidni Ilma. Is it okay son? We had here that -5/13x and + 12/13y = 3. We wrote this in standard form and we are just going to do the comparison.

[00:12:04]By comparing, we found that x is present in place of x, but what is the value of cos alpha? -5/13. Ok?

[00:12:10]Now y is present in place of y and the value of sin alpha is coming out to be 12/13.

[00:12:14]And what is coming in place of p?

[00:12:16]Three values ​​are coming. So see, you have completed it completely till here.

[00:12:20]Okay kids? Have you guys understood this? Ok? Take screenshots simultaneously. I will share the page again.

[00:12:24]You take a screenshot of it and then reverse the video and understand it and perform it yourself with your own hands.

[00:12:30]Ok? Now move forward. Now what are we doing next sir? Next we are going to do part number four. Look at this point slope form. Now the point slope form is coming. Look, I rewrote the equation.

[00:12:39]5x - 12y + 39 = 0 Now coming to point slope form. What should he do now? Now in point slope form this means we only have one point we need to do.

[00:12:48][sound of clearing throat] Convert two point intercept first into slope intercept form. Step number one: For the points row form, first find the value of y in the same way as you did before. That is, find the value of y from this equation.

[00:12:59]This is called bringing it to the form y = mx + c.

[00:13:02]Ok?

[00:13:04]You can bring this in the format y = mx + c.

[00:13:07]So look, 5x + 39 is right here.

[00:13:10]I took him there on 12th because he was negative here and became positive after going there.

[00:13:12]Well, you have to keep one thing in mind that you should not keep the value of y negative here. Ok? There should be complete possibility that it has to be made positive under all circumstances.

[00:13:20]Now I wrote it directly in such a way that you wrote the right hand side here and wrote this here.

[00:13:25]This will not change your sign. Please do n't spoil your concept. This is just the movement I made. Ok? I did nothing else.

[00:13:31]Now what will happen sir?

[00:13:33]Here I kicked 12 and this came. This same value has come again. So by comparing, when we compared, what value of slope are we getting? Look, this comparison means that by writing mx + c I have to see that the value of my slope is coming out to be 5/12. Ok? This is the first step. Now what will come at number two?

[00:13:47]Find the point on the line. Now you have to take a point above the line. Now you will say which line point to take? So my son, it is your wish. You have already done all these things before, what is the value of y when you put the value of x as zero?

[00:13:58]What is the value of y when the value of x is one put? Son, you have done this in 9th and 10th maths also.

[00:14:01]This was Chapter 8 of your old syllabus. Ok? In that also you had done this that you used to take points and check whether this point is taken or not or there were other things like this also. Ok? So let's suppose x = -3. You can take any value.

[00:14:13]I have taken x = -3. Now you [sound of clearing throat] will tell me why I took Teacher-3? So my son you take -2, take -1. You can take any value.

[00:14:22]Ok? Put this value of x in the equation.

[00:14:27]Put this value of x in the equation in your main equation. Look what I am going to do? 5x – 12y + 39 = 0. Now instead of 5x I am putting -3. Well, let me tell you this point first. This is an arbitrary point. This will be above your line.

[00:14:40]I have taken any point one. Because my this is coming my this is coming point slope form. Ok? That means that a point will have to be taken somewhere on your slope. Ok? Now look, here it was 53 and now it has become -15. -12y + 39 = 0. Now -15. Now look at this, bring the constant term next to the constant term. + Put 39 here only.

[00:14:59]Now the sign will not change here.

[00:15:01]Because you are not moving across the right hand side to the left hand side. You are clogging it up in one place. Meaning we are collecting like terms. And you dragged -12y a little bit and moved it here. = 0 sign changes kids when you do the across the equal sign movement. Meaning it is taken from the right hand side to the left hand side or from the left hand side to the right hand side. Now these -15 and +39 greater value signs have to come. 24 will come because 39 is positive and -12y = 0. Now I kick -12y and say, son, go there and become positive there. So after going there he became positive. If you want to find the value of y, then 12 will come and divide below it.

[00:15:32]Here, at this step too, children make mistakes under all circumstances. So this was coming up 12y.

[00:15:37]12y will be its divide under. So see what is coming next, we have son y = 24 = 2 so 12 * 1 = 12 12 * 2 = 24 so the value of y has come to two. This means that I have created my complete equation of x and y that I had put the value of x as -3 and I got the value of y as 2.

[00:15:56]So this point is my lie on the line. Ok? Look son, this is the procedure. If you take one point of x or y and find the value of the other, then what do they do if they are both? They come to your line.

[00:16:10]Ok? Now what to do in step number three? Use the point slope form. Now you had to remember the point slope form.

[00:16:16]Remember or not? The standard form has to be memorized.

[00:16:18]I have already explained this to you.

[00:16:20]So write the point slope form here.

[00:16:22]y − y1 = m x − x1. Ok? Let me highlight this again here.

[00:16:27]This is not some strange thing that has come before you. You have to learn this son for all MCQs. Ok?

[00:16:34]I explained all these things to you in the previous video.

[00:16:35]Now by substituting, what are we going to substitute in this?

[00:16:39]Look here in this equation we just found the value of m. You had calculated the value of slope, this value is 512. We're going to put this into this equation right there. m = 512 and what was this x1 y1 point coming to us? Look at this x1 y1 I wrote this because it's a single point.

[00:16:55]I took just one point.

[00:16:56]I didn't take two points on its slope, did I? So I will name it x1 y1 and this point here in the form of order pair, I will write here -3 2 and my open brackets will be closed.

[00:17:04]Ok? Now I am going to put in this equation. This is my point and this is my slope. Look, what is the value of y1 coming here instead of y - y1? Two to came equal to slope of m value came 512.

[00:17:17]What do we have coming here? Look, this equation has x. This this x x has come. The minus sign has come. And what is the value of x1? The value of x1 I have is -3. Look, this is my x1 and this is my y1. So this came out to be -3. Now you my children, solve this comfortably. y - 2 = 51 12 x is arrived at. Minus minus plus came. Three has arrived. So what has come to us? There is no need to solve this further. You have done this much.

[00:17:40]We have become very happy. So write it here. Which is the required equation. Ok? So you can highlight it with great fun by doing it like this, like this, like this, by making a box here.

[00:17:49]Ok? You have understood this little thing. The story is being completed in three steps. By returning the video, you will create a compatibility for yourself as to what you have to do for it.

[00:17:59]Ok? Now look ahead at the two point form.

[00:18:01]Number five is coming. Two point form. Now what are you going to do for the two point form? We wrote the equation. For this you have to take two points on the line. Because this two point one is coming. She was coming with one point.

[00:18:10]This is two points. Now for this we will take two points. It's the same procedure my children. Nothing can bother you in life.

[00:18:15]If you make up your mind that we have to learn this and we will not learn it considering it a burden. Now what is coming in step number one? Find the two points on the line. Now we have to take two points. First, in the previous one, we had taken one point in this one above.

[00:18:26]So we will use that only.

[00:18:28]We are not fools to keep scoring new points again and again. So look, I'm going to do the same thing again. x = -3. By putting the same in it, I found the value of y to be two in the entire equation. Till here the same procedure is going on. Which is what you did in the previous one. So do this here, pick it up from there and make a photocopy.

[00:18:42]Ok? Now let x = 9. Now I have taken this as a positive point by my own choice.

[00:18:46]x = 9 for the second point. What have I written here? That for the second point I took nine. Now put nine in it.

[00:18:51]By putting nine, this is a completely childish thing, children. And I have also told you that the arithmetic operation is coming simple. So y equal to what are we getting? From this we get 12 * 1 = 12 12 7 = 84 7.

[00:19:01]So what did we get at the second point?

[00:19:02]Look, in case of order pair, you people see that 9 and 7, now I have got one point here and one point there. Two points have come.

[00:19:08]I will just remember the equation by heart. I will do the plotting in it. Use the two point form. Here you have y - y1 over y2 - y1 = x - x1 x2 - x1. This is your original equation.

[00:19:20]How to remember this? y - y1 minus y1. Then go down and subtract y1 from y2 in the denominators. So y - y1 over y2 - y1 and put the same x version of this over here. x - x1 is what I am calling its version of the same x.

[00:19:36]x - x1 x2 - x1 okay? What will you do now? Then finally you will kick the denominator below this because we do not want to deal with fractions.

[00:19:44]Fractions are difficult to deal with in maths.

[00:19:45]So tell him, son, go there and have fun with them and write that poor guy's whole in brackets so that whatever he has is not disturbed and you come to know that this will be multiplied with this whole.

[00:19:54]Ok? You kicked it over there and put the poor guy all the way back into his house.

[00:19:59]This is being multiplied by this.

[00:20:00]What do you want to do now, children? By substituting two of your points x1 y1, what points are you getting? -3 and 2 has come and the point x2 was 9 and 7, don't worry, I am turning the page back again, see, the first point is -3 and 2, we will name it x1 and y y1 and this second point which was taken just below, 9 and 7, the seven value of x was taken out by taking 9, so we will name it x2 and y2, so this is what I have put here, see x1 y1 - 3 and 2 x2 y2 9 and 7, now I am going to put this in the equation which I have made, y - 2, see what is the value of y1 coming out, look here, you will have to look carefully, the value of y1 is coming out because a small mistake at this stage spoils all the hard work done in the past.

[00:20:38]So look carefully that the first pair that comes up is x1 and y1. The second pair that comes up is x2 and y2. So the value of y1 is put to. Then what did I put sir? So here y2 - y1. Now what do I have y2?

[00:20:49]I will look carefully. Seven is coming. Seven written minus and what is this coming to us sir? y1 what is coming? y1 Look carefully.

[00:20:55]This is y1 so it is sitting at place two. Two has come. And in the same way, all your values, this minus sign that is coming, son, will be its sign. What is this x - x1 x will remain the same, what is the minus sign x1 we have here, look carefully this is x1 i.e. -3 so we will have to write -3 in brackets because there is already a minus outside and a minus is also attached to it, so whenever there is a minus etc. then you have to be very conscious that there will be a mistake here, so I have to do it very carefully, put it in brackets, okay because minus after going ahead minus will multiply, so the same thing happened below also, you put the value in x2 - x1, see this is also happening in the same way, now you brought it down, similarly 2 went away from 7, 5 came out, x this became minus minus + 3, what is happening below, 9 minus minus + 3, so what is this that we have? y - 2 = 5 And what's this coming from above? x + 31 here we go and you kick it back again. Tell Five, son, you have had a lot of fun with him, now go back to your place, go back to your home.

[00:21:46]Back from where we had lifted it from below and taken it up, we had got it multiplied.

[00:21:50]Tell him bye son, go downstairs. Now y - 2 5 = x + 312, both of these are the same form. So you can write it like this also.

[00:21:58]You can also write to me like this. That's it. This is complete for you my children. Ok? Now after this let us move forward.

[00:22:04]Ok? Symmetric form is coming. Whatever happens after this is not the end of the story.

[00:22:08]Ok? Look at this last one, this one is coming to us with six. 5x - 12y + 39 = 0 Here it is coming to you, kids. So what's the first step we need to do in symmetric form? Find two points on the line.

[00:22:19]We had taken two points last time. That's why I have written as found earlier, that I have already found these. -3 and 2 are named x1, y1 and behind them are nine and seven. You guys have just added two points. That's what I'm putting again.

[00:22:30]So what will come in step number two? Find the direction ratios.

[00:22:33]Look son, now I am making you do this symmetric form in two ways.

[00:22:36]Ok? This first one is a very easy method. After this I will also get the second one done which your teacher might have made you do and which is mentioned in your book. Ok?

[00:22:44]Look here how I am finding it from Find the Direction Ratio.

[00:22:45]We find out a by doing x2 - x1.

[00:22:49]Just remember this thing that a is x2 - x1. And b is y2 - y1. Ok? Now put the value here.

[00:22:56]What is x2? From here, when you have written this carefully x1, y1, x2, y2, then there will be no mistake on your part and check the counter even after putting it there. So this x2 is coming to me nine. The minus sign has come. x1 How much am I getting? -3 is coming.

[00:23:08]So I will put this in brackets.

[00:23:09]Ok? So minus minus will become plus. 9 + 3 is 12. Similarly, now I have to calculate b. So y2 - y1 for b.

[00:23:15]Now what is y2 coming to me? Sir, look carefully. Seven is coming. The minus sign has come. How much is y1 coming? Two is coming. So 7 - 2 equals 5. So what are the direction ratios we come up with? Just look carefully. A 12 has arrived. Write that in the first one.

[00:23:26]Write it in the first place and you get five.

[00:23:28]Ok? What should I do now? Use the symmetric form. I'm going to write the symmetric form.

[00:23:31]The symmetric form of a line through x1 y1 with direction ratios ab is what is it? x - x1 a okay? And = y - y1 over b If you want to find the symmetric form from the symmetric ratio, sorry, you want to find the symmetric form from the direction ratio, then you can use this equation.

[00:23:48]Ok? So this is coming in an easy way. Ok? Make him a star.

[00:23:52]This is coming in an easy way. x - x1 over a y - y1 over b means you should understand that here you did the reverse work x2 - x1 but here you have to do x - x1 and this y - y1. Now I am going to put the values ​​in this equation by substituting the values ​​of x1 and y1.

[00:24:09]Look here son, what value of x1 y1 are you getting? This is coming to us, what is this name? Look here, how much x1 y1 are we getting? -3 and 2, this first value which is the first point, my a = 12 is coming and b = 5 is coming. Ok? The five values we just found are direction ratios. The sign of x becomes the minus sign and the value of x1 will have to be written in the bracket -3. Over 12 = y arrived. y minus, look, the minus sign is 2 5. Now by doing a simple operation here, you have got x - + 312 y - 2 5, this is complete. Ok? Here you have your symmetric form. Now I have written more. This is what you have been taught to do. Okay, right? He was in Easy Way. Exactly the values ​​of SIM a and b were calculated and the answer was put in the formula.

[00:24:52]Now look what is coming here? Symmetric form 5x - 12y + 39 = 0 Now whatever procedure you use, the examiner will not cut your marks because see it has become conceptual based.

[00:25:02]Everything has become SLO. Ok? So now get free from the tension of this thing. And like those level J levels, you people also have to study in the same way. 5x + 39 = Look what we are doing here? Kick 5x + 39 and 12y so that you have to find the value of y, son. 12y went there and tested positive. Now I wrote it directly like that. 12y = so and the value of y is divided by 12 aa.

[00:25:22]Ok? Now y = 51x means I am bringing it to the form y = mx + c.

[00:25:28]In slope intercept form + 391, look, this is how the bean came out. Now look here y = mx + c, now what is the value of m coming out?

[00:25:36]tell me fast. The value of m we are getting is 512. See for yourself whether the value of m that has been calculated is 512 or not? Yes, 512 is definitely coming. Now let me give you a new concept from here. Please be attentive. Listen carefully. 512 has come.

[00:25:50]So what will this be equal to? The value of m will be equal to tan tan alpha. Remember I hid you behind me. When I had put my hand in the previous video that we will talk about this later. Ok? I did not understand what I wanted to tell you there. I said I will tell you when I get this question asked.

[00:26:04]tan alpha is coming. This is equal to tan alpha.

[00:26:05]How? Now look, I am going to explain this concept here. How?

[00:26:09]Look, here comes the x and y axis. This was your line going. You drew this projection and what value is it coming out? See five. What's coming up Five? Listen to me.

[00:26:16]What is tan tan theta equal to? tan theta we have is equal to perpendicular over base. Ok?

[00:26:23]Why? Why? Because you can remember it like this that tan theta, that is, call it tan theta, call it tan alpha, is equal to perpendicular over base.

[00:26:32]I don't know whether you guys know this or not that you can remember the values ​​of sin theta, cos theta and tan theta like this sin theta Some people have curly brown hair through proper brushing. Ok?

[00:26:42]That some people have sin theta which is perpendicular over hypotenuse. So Some People Have Happened. Took his first initial.

[00:26:48]And what will come to us as cos theta? Curly C for curly cos theta brown B for base over curly brown hair H for hair, it is showing hypotenuse and through proper brushing, see, I have done this through proper brushing here, that is perpendicular over base, I will explain this concept to you again by making another video, now you guys have to prepare quickly, okay now see what I have done, this is perpendicular and what is this, it is base below, so because of 5 over 12, this will be equal to 10 tan alpha, okay now if I take this out because see, I have the value of five as well as the value of 12, but I do not have the value of hypotenuse, this is perpendicular. This is a 90° angle. The one below is the base.

[00:27:23]And what is this, your son? This is your hypotension. Ok? So this has become a right angle triangle. We can apply the Pythagorean theorem to this. Which tells us that the square of the hypotenuse is equal to the square of the base plus the square of the perpendicular.

[00:27:33]Ok? Now look here, should I explain to him what is coming to you? The same rise, this slope, is rise over run. Look at the meaning of rise over runs, first you will take the value of rise, the value of five over runs will be 12 below. The same thing is happening here.

[00:27:46]Call it perpendicular over base. Call it rise over run.

[00:27:48]So this is going to be equal to tan apha. Now what are we going to do from here? The values ​​were 5 and 12.

[00:27:53]We're going to take the value of its hypotenuse.

[00:27:55]So look at this x², let's suppose you call it x. The value which needs to be calculated in math is called x. I have always been saying this since childhood. Ok?

[00:28:03]This x never leaves us alone. So look at this, the square of the hypotenuse = the square of 12 plus what is it coming out to be? Square of 5. x² = 12² 144 becomes 5² 25. So x² equals to when we add these two, it gives 169. If you want to get rid of the square, then you will have to take the under root of the square root. So when we took the square root, x came out here and we got 13 of 169. Is it okay son? So what value of x have you taken? 13 You have taken the value. Now that you have taken the value, please complete this triangle. The poor guy was feeling sad at first because he had two friends. There is no third partner. So look, when you have taken the value here 13, 5 and 12 are coming. Now you take that out of it. Find sin apha also, find cos alpha also. sin apha I just told you that some people have to remember like this. So sin alpha is equal to perpendicular over hypotenuse.

[00:28:44]Some people have cos theta which is equal to base over hypotenuse.

[00:28:48]Curly brown hair, remember your coding by holding the initials of all these.

[00:28:52]All your teachers must have told you this also. Okay, right? There is nothing new. Ok? sin alpha = p over h. That is, perpendicular over hypoten, what is all this perpendicular? There's five here. Put a value of five. The value of hypotenuse you have just calculated is 13. Put the value here.

[00:29:05]Now cos alpha which is coming out is equal to base over hypotenuse. So this is the base on which the angle lies. So this is the base because two angles are lying on it.

[00:29:12]Alpha is also on this and the 90° angle is also on this.

[00:29:13]So this comes to 12. What is the value of over hypotenuse coming? 13 is coming.

[00:29:17]Hypotension is always this swing, son, with the slide. Ok? Now one point is online, now you had already taken one point, right?

[00:29:23]Look, the first point taken was -3 and 2, write them here and x1 y1 comes. Now you are going to put its equation.

[00:29:29]So you have written down its equation which you have memorized in your book in its symmetric form.

[00:29:32]This equation is x - x1 over cos alpha = y - y1 over sin apha = 1 Now you put the value here. The sign of x has come, the sign of minus has come.

[00:29:42]What is the value of x1? -3 Look from here, this -3 is coming. This will become x - + 3 on the put side.

[00:29:47]Below is cos apha. I am not putting the value of cos apha at this stage. Right now I am just putting the above values. The value of y - y1 is coming out to be 2. I put this over sin apha = 1. Now in the next step I am going to put the values ​​of cos apha and sin apha.

[00:29:59]Ok? The value of cos sin apha is coming out to be 51 13.

[00:30:02]Look above, the value of cos alpha is coming out to be 121 13.

[00:30:04]So I put 121 13 here.

[00:30:06]5/13 putted. I don't have to solve this because my required equation is in front of you. So I have changed my equation into symmetric form.

[00:30:15]Okay kids? So, till here, I think you must have understood the concept of Chapter Four very well and if I could be of any help to you, then I am very happy about it. Ok? Now in my next video I will try to make MCQs of integration and derivative for you guys or to explain its concepts.

[00:30:33]But son it will take a lot of time to not only develop our data but also to create the data here. Let me sit and write in the written form first. After that I will record you. Then I'll make a thumbnail of it. Meaning my team should do all this work and make thumbnails, make everything, then upload it, everything. So it's a very lengthy procedure. Ok? It will take time. So we also want its output from you people that you should share it as much as possible so that our aim is that in such an expensive era, good and quality education should be available at the doorstep of every child and they do not face any tension. Neither notes nor anything else, but they should get good quality education. Okay kids? See you till next time to do it.