An ellipse passes through the foci of the hyperbola, $9x^2-4y^2=36$ and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\large\frac{1}{2}$, then which of the following points does not lie on the ellipse ?

Question

$\begin{array}{1 1} (\sqrt {13},0) \\ \bigg(\frac{\sqrt{39}}{2} , \sqrt 3 \bigg) \\ \bigg( \frac{1}{2} \sqrt {13}, \frac{\sqrt 3}{2} \bigg) \\ \sqrt{\frac {13}{2}},\sqrt {6} \bigg) \end{array} $