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Q.

A variable line whose slope is -2 cuts x and y axes respectively at points A and C. A Rhombus ABCD is completed. Such that the vertices B lies on the line y=x, then the locus of the vertex D is

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a

x+y+2=0

b

x+y+3=0

c

x+y=0

d

x+y-1=0

answer is C.

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Detailed Solution

Let the line be xa+yb=1⇒b=2aLet B be α,α, D be (h,k)∴h+α=a k+α=b∴ABCD is a rhombus α−kα−h×b−a=−1Locus of (h,k) is x+y=0
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