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 $\frac{1}{2}$ , then which of the following points does not lie on the ellipse ?

Question

( A ) $(\frac{1}{2} \sqrt{13}, \frac{\sqrt{3}}{2})$
( B ) $(\sqrt{\frac{39}{2}}, \sqrt{6})$
( C ) $( \sqrt{13}, 0)$
( D ) $(\frac{\sqrt{39}}{2}, \sqrt{3})$