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Question

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



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(yt2t2)=1 or ty22t2+1=0.
For common tangent, it should have equal roots.
4t44t=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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