The normal at a point P on the ellipse $$x^2 + 4y^2 = 16$$ meets the x-axis at Q. If M is the mid point of the line segment PQ, then the locus of M intersects the latus rectums of the given ellipse at the points

A

$$\left(\pm \frac{3\sqrt{5}}{2}, \pm \frac{2}{7}\right)$$

B

$$\left(\pm \frac{3\sqrt{5}}{2}, \pm \frac{\sqrt{19}}{4}\right)$$

C

$$\left(\pm 2\sqrt{3}, \pm \frac{1}{7}\right)$$

D

$$\left(\pm 2\sqrt{3}, \pm \frac{4\sqrt{3}}{7}\right)$$