Mathematics

Problem

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 latusrectum of the given ellipse at the points a.

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

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

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

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