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Find the equation of the common tangent ...

Find the equation of the common tangent to the curves `y^2=8x` and xy=-1.

A

3y = 9x + 2

B

y = 2x + 1

C

2y = x + 8

D

y = x + 2

Text Solution

Verified by Experts

The correct Answer is:
D
Tangent to the curve `y^(2) = 8x` is `y = mx + (2)/(m)`. So it must satisfy xy = - 1
`implies x (mx + (2)/(m)) = - 1 implies mx^(2) + (2)/(m) x + 1 = 0`
Since, it has equal roots.
`:. D = 0`
`implies (4)/(m^(2)) - 4m = 0`
`implies m^(3) = 1`
`implies m = 1`
Hence, equation of common tangent is y = x + 2
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