The normal at a point $P$ on the ellipse $x^2+4 y^2=16$ meets the $x$-axis at $Q$. If $M$ is the mid point of the line segment $P Q$, then the locus of $M$ intersects the latus rectums of the given ellipse at the points
The normal at a point $P$ on the ellipse $x^2+4 y^2=16$ meets the $x$-axis at $Q$. If $M$ is the mid point of the line segment $P Q$, then the locus of $M$ intersects the latus rectums of the given ellipse at the points
- [IIT 2009]
- 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
$\left( \pm 2 \sqrt{3}, \pm \frac{4 \sqrt{3}}{7}\right)$
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Let $P$ be an arbitrary point on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ $a > b > 0$. Suppose $F_1$ and $F_2$ are the foci of the ellipse. The locus of the centroid of the $\Delta P F_1 F_2$ as $P$ moves on the ellipse is
- [KVPY 2010]
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