Question

Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and (i) through the point (−1, 2) (ii) Parallel to x−y+5 = 0 (iii) Perpendicular to x − 2y + 1 = 0. ​

Answer 1

Answer:

To find the point of intersection of the lines we have to solve them Substituting

x = -1 in equation

(2) we get -5 + 2y = -7 ⇒ 2y = – 7 + 5 = -2 ⇒ y = -1 So the point of intersection is (-1, -1) (i)

Now

(ii) Equation of a line parallel to x – y + 5 = 0 will be of the form x – y + k= 0. It passes through (-1, -1) ⇒ -1 + 1 + k = 0 ⇒ k = 0. So the required line is x – y = 0 ⇒ x = y.

(iii) Equation of a line perpendicular to x – 2y+ 1 = 0 will be of the form 2x + y + k = 0.

It passes through (-1, -1) ⇒ -2 – 1 + k = 0 ⇒ k = 3. So the required line is 2x + y + 3 = 0