JEE Main 2022 — Hyperbola Question with Solution

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?