If the curves
Question:

If the curves $\frac{x^{2}}{\alpha}+\frac{y^{2}}{4}=1$ and $y^{3}=16 x$ intersect at right angles, then a value of $\alpha$ is :

1. $\frac{4}{3}$

2. $\frac{3}{4}$

3. $\frac{1}{2}$

4. 2

Correct Option: 1

Solution: