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Find the equation of the common tangent to the curves `y^2=8x` and xy=-1.A. 3y = 9x + 2B. y = 2x + 1C. 2y = x + 8D. y = x + 2 |
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Answer» Correct Answer - 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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