The equation of common tangent to Parabola ` y ^2 = 8x and y = - x ^ 2 ` is :

Options

A. ` 2x - y + 1 = 0 `
B. ` x - 2 y + 1 = 0 `
C. ` 2x + y + 1 = 0`
D. ` x + 2y + 1 = 0 `

Answer

A

Explanation

`y^(2) = 8x , x^(2) = - y`
Common tanget ` y = mx + (2)/(m) -= y = mx + (m^(2))/(4)`
`rArr " " (2)/(m) = (m^(2))/(4) rArr m^(3) = 8 rArr m = 2`
CT , y = 2x + 1 ` " "rArr " " 2x - y + 1 =0`