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The equation of common tangent of the curve `x^(2) + 4y^(2) = 8` and `y^(2) =4x` areA. x-2y + 4 = 0 , x + 2y + 4 = 0B. 2x-y + 4 = 0 , 2x + y + 4 = 0C. 2x-y +2 = 0 , 2x + y + 2 = 0D. None of these |
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Answer» Correct Answer - A Ellipse `(x^(2))/(8) + (y^(2))/(2) = 1 ` Equation of tangent y = mx `pm sqrt(8m^(2) +2) ……(1)` and parabola `y^(2) = 4x` Equation fo tangent `implies y = mx +(1)/(m) " " …..(2)` for common tangent `pm sqrt(8m^(2) + 2) = (1)/(m)` `implies 8m^(2) + 2 = (1)/(m^(2))` `implies 8m^(4) + 2m^(2) - 1 = 0` `implies (4m^(2) - 1) (2m^(2) + 1) = 0 implies m = pm(1)/(2)` `therefore Eq^(n)` of common tangent `y = pm (1)/(2) x pm 2 ` `implies x - 2y + 4 = 0` and x + 2y + 4 = 0 |
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