Equation Of A Common Tangent To The Curves y2 = 8x and xy = –1 Is 

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Equation of a common tangent to the curves y2 = 8x and xy = –1 is 


Correct option is

x + 2

Equation of a tangent at (at2, 2at) to y2 = 8x is ty = x + atwhere 4a = 8 i.e., = 1.

⇒ ty = x + at2 which intersects the curve xy = –1 at the points given by  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 x + 2.



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