Answer :

Given:


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


To 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.


Explanation:


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


x + 2y + 3 + λ(3x + 4y + 7) = 0


(1 + 3λ)x + (2 + 4λ)y + 3 + 7λ = 0


y


The required line is perpendicular to x y + 9 = 0 or, y = x + 9



λ = -1


Required equation is given below:


(1 3)x + (2 4)y + 3 7 = 0


x + y + 2 = 0


Hence, required equation is x + y + 2 = 0


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