JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 74

Let the hyperbola $H:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ pass through the point $\left(2\sqrt2,-2\sqrt2\right)$. 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 ?