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Question

# A line passing through point A (-5, -4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x−y−5=0 at B,C and D respectively If (15AB)2+(10AC)2=(6AD)2, then the equation of line is

A
2x + 3y + 22 = 0
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B
5x - 4y + 7 = 0
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C
3x - 2y + 3 = 0
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D
3x + 2y + 3 = 0
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Solution

## The correct option is A 2x + 3y + 22 = 0(ABcosθ−5,ABsinθ−4) lie on the line x + 3y + 2 = 0 ⇒AB cos theta−5+3(AB sinθ−4)+2=0⇒cosθ+3sinθ=15AB –––––––(1) (AC cosθ−5,AC sin θ−4) lie on the line 2x + y + 4 = 0 ⇒2 cosθ+sinθ=10AC –––––––(2) (AD cosθ−5,AD sin θ−4) lie on the line x - y - 5 =0 ⇒cosθ−sinθ=6AD –––––––(3) (15AB)2+(10AC)2=(6AD)2⇒Tanθ=−23=m⇒y+4=−23(x+5)⇒2x+3y+22=0

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