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Question -

Find the equation of a straight line passing through the point of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 and perpendicular to the straight line x – y + 9 = 0.



Answer -

Given:

x + 2y + 3 = 0 and 3x+ 4y + 7 = 0

The equation of thestraight line passing through the points of intersection of x + 2y + 3 = 0 and3x + 4y + 7 = 0 is

x + 2y + 3 + λ(3x+ 4y + 7) = 0

(1 + 3λ)x + (2 + 4λ)y+ 3 + 7λ = 0

The required line isperpendicular to x − y + 9 = 0 or, y = x + 9

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