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Let \( a, b \) and \( \lambda \) be positive real numbers. Suppose \( P \)
\( \mathrm{P} \) is an end point of the latus rectum of the parabola \( y^{2} \)

W \( =4 \lambda x \), 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) \( \frac{1}{\sqrt{2}} \)
(2) \( \frac{1}{2} \)
(3) \( \frac{1}{3} \)
(4) \( \frac{2}{5} \)
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