JEE Math Practice Question

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?

1. A.$$(2 \sqrt{3}, 3 \sqrt{2})$$
2. B.$$\mathbf(3 \sqrt{3},-6 \sqrt{2})$$
3. C.$$(\sqrt{3},-\sqrt{6})$$
4. D.$$(3 \sqrt{6}, 6 \sqrt{2})$$