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 (A) $\frac { 1 } { \sqrt { 2 } }$ (B) $\frac { 1 } { 2 }$ (C) $\frac { 1 } { 3 }$ (D) $\frac { 2 } { 5 }$
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\\
(A) $\frac { 1 } { \sqrt { 2 } }$\\
(B) $\frac { 1 } { 2 }$\\
(C) $\frac { 1 } { 3 }$\\
(D) $\frac { 2 } { 5 }$