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Question

The mirror image of y2=4x about the line xy+1=0 is

A
(x1)2=4(y+1)
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B
(x+1)2=4(y+1)
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C
(x+1)2=4(y1)
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D
(x1)2=4(y1)
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Solution

The correct option is C (x+1)2=4(y1)
Any point on y2=4x is P(t2,2t).
Let the image of P about xy+1=0 be (h,k).
ht21=k2t1=2(t22t+1)12+(1)2
ht2=k+2t=(t22t+1)
h=2t1 and k=t2+1
Eliminating t, we get
k1=(h+12)2
Hence, locus of P is (x+1)2=4(y1)

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