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Question

The equations of the diagonals of the square formed by the pairs of straight lines 3x2+8xy3y2=0 and 3x2+8xy3y2+2x4y1=0 are?

A
x=2y,4x+2y+1=0
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B
2x+y=0,2x=4y+1
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C
x=2y,2x=4y+1
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D
2x+y=0,4x+2y+1=0
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Solution

The correct option is B 2x+y=0,2x=4y+1
Given pair of straight lines are 3x2+8xy3y2=03x2+8xy3y2+2x4y1=0(2) Partial differentiate with respect to x6x+8y+2=0(3) Partial differentiate with respect to y8x6y4=0 (4)


To find point of intersection of (3) and (4) x=525=125;y=25 To find equation of diagonals slope of AC=2/501/50=2 Slope of DB=y=2x=12
Equation of BD: y+15=12(x110)10x20y=52x4y=1 Equation of AC which is 1 to BC4x+2y=k(15,110)45+15=kk=1AC:2x+y=0 then, (B) is the correct option.

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