Find the distance between lines 2x3y 5 0 and 6x 9y 5 0 17375

Name: find the distance between lines 2x3y 5 0 and 6x 9y 5 0 17375
Uploaded: 2022-06-09T05:36:50-08:00
Duration: 3 min 12 s
Channel: Ankit Singh
Description: find the distance between lines 2x3y 5 0 and 6x 9y 5 0 17375

Transcript

00:01 So in this question basically we need to find distance between the given lines.

00:05 So these lines are parallel because slope of the first line that is minus x coefficient, minus of x coefficient upon y coefficient that is minus 2 by 3.

00:17 And in the case of second line, minus of x coefficient upon y coefficient is simply minus 2 upon 3.

00:25 So in this case we can say that m1 is equal to m2 so lines are parallel.

00:31 Now in the case of two lines are parallel, suppose we have two lines like a1x plus b1y plus v1y plus c1 is equal to 0 and second line is simply a1x a1x plus v1y plus c2 is equal to 0.

00:55 So distance between these lines is simply fine with the help of root of mod of c1 minus c2 mod of c1 minus c2 root of a1 square plus b1 square so first we will make these coefficient as same in order to do that we will just divide by 3 in the second so this will give us simply this will give us simply to x plus 3y minus 5 upon 3 so this is the second equation this is the second equation and i'm just rewriting the first equation again and that is simply 2x plus 3y minus 5 is equal to 0 so this is our first condition first line now in order to find distance between these two line we will use this formula because both lines are in this form so distance will be simply c1 minus c2 so in this case minus 5 upon 3 minus of minus 5 mod upon root of a square plus b squared that is 4 plus 9 so this will be simplified as minus 5 upon 3 plus 5 and mod of root of 13 root of 13 so we can simplify further so from here we can say that t will be simply minus 5 upon 3 plus 5 is simply minus 10 upon 3, minus 10 upon 3 upon root of 13 upon root of 13.

02:39 So from where we can say that value of d is mod of minus 10 by 3 is simply 10 by 3...

Question

Find the distance between lines 2x+3y -5 =0 and 6x + 9y – 5 =0

Question

Find the distance between lines 2x+3y -5 =0 and 6x + 9y – 5 =0

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