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$The locus of image of the point (λ^{2}, 2 λ) in the line mirror x - y + 1 = 0 where λ is a parameter is$

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4(y+1)=(x+1)2

4(y-1)=(x-1)2

4(y+1)=(x−1)2

4(y-1)=(x+1)2

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detailed solution

Correct option is D

Image of λ2,2λ in the line mirror x−y+1=0 is h−λ21=k−2λ−1=−2λ2−2λ+12⇒h+1=2λ………… And k=λ2+1……… (2) Putting value of λ from (1) into (2), we get k−1=h+122 locus is 4(y-1)=(x+1)2

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The locus of image of the point λ2,2λ in the line mirror x−y+1=0 where λ is a parameter is

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$The locus of image of the point (λ^{2}, 2 λ) in the line mirror x - y + 1 = 0 where λ is a parameter is$