Let the hyperbola \( H: \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 \) 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
