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

• Correct answer
  A

  $\frac{1}{\sqrt{2}}$
• B

  $\frac{1}{2}$
• C

  $\frac{1}{3}$
• D

  $\frac{2}{5}$

Hence, the correct answer is option: 'A'.