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Equation of a common tangent to the curves $y^{2} = 8 x$ and $x y = - 1$ is

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3y=9x+2

y=2x+1

2y=x+8

y=x+2

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detailed solution

Correct option is D

Equation of a tangent at at2,2at to y2=8xty=x+at2 where 4a=8 i.e. a=2⇒ ty=x+2t2 which intersects the curve xy=−1 at the points given by xx+2t2t=−1 clearly t≠0 or x2+2t2x+t=0 and will be a tangent to the curve if the roots of this quadratic equation are equal, for which 4t4 – 4t = 0⇒ t = 0 or t = 1 and an equation of a common tangent is y = x + 2.

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