Let the hyperbola H: x^2/a^2-y^2/b^2=1 pass through the point (2 √ 2,-2 √ 2 ). A parabola is drawn whose focus is same as the focus of H with…

Let the hyperbola $\displaystyle H: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ pass through the point $\displaystyle (2 \sqrt{2},-2 \sqrt{2})$. A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H . If the length of the latus rectum of the parabola is e times the length of the latus rectum of H , where e is the eccentricity of H , then which of the following points lies on the parabola ?