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Question

# The equations of the diagonals of the square formed by the pairs of straight lines 3x2+8xyâˆ’3y2=0 and 3x2+8xyâˆ’3y2+2xâˆ’4yâˆ’1=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+8xy−3y2=03x2+8xy−3y2+2x−4y−1=0−(2) Partial differentiate with respect to x⇒6x+8y+2=0−(3) Partial differentiate with respect to y⇒8x−6y−4=0− (4) To find point of intersection of (3) and (4) x=525=125;y=−25 To find equation of diagonals slope of AC=−2/5−01/5−0=−2 Slope of DB=y=−2x=12 Equation of BD: y+15=12(x−110)⇒10x−20y=5⇒2x−4y=1 Equation of AC which is 1 to BC⇒−4x+2y=k(−15,110)⇒45+15=k⇒k=1AC:2x+y=0 then, (B) is the correct option.

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