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Question

The image of the curve y2=4x in the line x+y+2=0 is

A
(x+2)2+4(y1)=0
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B
(x+2)2+4(y+2)=0
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C
(x1)2+4(y1)=0
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D
None of these
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Solution

The correct option is C (x+2)2+4(y+2)=0
Any point on y2=4x can be represented by P(t2,2t) where t is a variable parameter.
If P(x1,y1) is the image of P on x+y+2=0(AB)
PPAB and the mid-point of PP lies on AB.
y12tx1t2=1 and x1+t22+y1+2t2+2=0
i.e. x1y1=t22t and x1+y1=(t2+2t+4)
Adding 2x1=4t4t=(x1+2)2
From x1y1=(x1+2)24+(x1+2)
The locus of (x1,y1) is (x+2)2+4(y+2)=0

Hence, option B.

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