The equation to the line touching both the parabolas `y^2 =4x` and `x^2=-32y` is

Options

A. `(1)/(2)`
B. `(3)/(2)`
C. `(1)/(8)`
D. `(2)/(3)`

Answer

A

Explanation

Let the tangent to parabola be y = mx + a/m, if it touches the other curve, D = 0, to get the value of m.
For parabola `y^(2) = 4x`
Let `y = mx + (1)/(m)` be tangent line and it touches the parabola `x^(2) = - 32y`
`:. X^(2) = - 32 (mx + (1)/(m))`
`implies x^(2) + 32 mx + (32)/(m) = 0`
D = 0
`:' (32 m)^(2) - 4 ((32)/(m)) = 0 implies m^(3) = 1//8`
`:. m = 1//2`