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 parabo…

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 \(H\) 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?

[JEE Main 2022, 28 Jul (Shift 2)]