JEE Math Practice Question

Let $a, b$ and $\lambda$ be positive real numbers. Suppose $P$ is an end point of the latus rectum of the parabola $y^{2}=4 \lambda x$, and suppose the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ passes through the point $P$. If the tangents to the parabola and the ellipse at the point $P$ are perpendicular to each other, then the eccentricity of the ellipse is

1. A.$\frac{1}{\sqrt{2}}$
2. B.$\frac{1}{2}$
3. C.$\frac{1}{3}$
4. D.$\frac{2}{5}$