Let PQ be a focal chord of the parabola y^2=4 x such that it subtends an angle of (π)/2 at the point (3, 0). Let the line segment PQ be also a focal…

Let PQ be a focal chord of the parabola $\displaystyle y^2=4 x$ such that it subtends an angle of $\displaystyle \frac{\pi}{2}$ at the point $\displaystyle (3, 0)$. Let the line segment PQ be also a focal chord of the ellipse $\displaystyle \mathrm{E}: \frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1, \mathrm{a}^2>\mathrm{b}^2$. If e is the eccentricity of the ellipse E, then the value of $\displaystyle \frac{1}{\mathrm{e}^2}$ is equal to :