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Question

The equation of the common tangent to the curves is y2=8x and xy=−1 is


A

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B

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C

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D

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Solution

The correct option is D


Any point on y2=8x is (2t2,4t) where the tangent is yt=x+2t2.
Solving it with xy=−1,y(yt−2t2)=−1 or ty2−2t2+1=0.
For common tangent, it should have equal roots.
∴4t4−4t=0 ⇒t=0,1.
∴ The common tangent is y=x+2, (when t=0, it is x=0 which can touch xy=-1 at infinity only).


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