Mathematics - Application of Derivative Question with Solution | TestHub

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