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