Let L_1: x+2y-3=0, L_2: 2x-y+4=0 be two straight lines

MATHEMATICS · Subjective · CBSE · Mathematics · Straight Lines · Straight Lines

Problem

Let

L_1: x+2y-3=0, \qquad L_2: 2x-y+4=0

be two straight lines. Every line passing through their point of intersection can be written in the family form

L_1 + p\,L_2 = 0,

where

p

is a real parameter. Another line is given by

L_3: 3x - y + 5 = 0.

(i) Obtain the equation of the family of lines passing through the intersection point of

L_1

and

L_2

. (ii) Determine the value of

p

for which the member of the family is perpendicular to

L_3

. (iii) For that value of

p

, find the coordinates of the point where the perpendicular line obtained in part (ii) intersects

L_3