The slope of the line touching both the parabolas y^{2} = 4x and x^{2} = -32y is

- 1/2
- 2/3
- 3/2
- 1/8

**Answer**

Equation of the tangent at A(t^{2}, 2t)

yt = x + t^{2} is tangent to x^{2} + 32y = 0 at B

x^{2} + 32(x/t + t) = 0

x^{2} + 32x/t + 32t = 0

(32/t)^{2} - 4(32t) = 0

32(32/t^{2} - 4t) = 0

**The correct option is A.**