The equation of common tangent of the curve `x^(2) + 4y^(2) = 8` and `y^(2) =4x` are

Options

A. x-2y + 4 = 0 , x + 2y + 4 = 0
B. 2x-y + 4 = 0 , 2x + y + 4 = 0
C. 2x-y +2 = 0 , 2x + y + 2 = 0
D. None of these

Answer

A

Explanation

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