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?