c for sure
The normal at a point P on the ellipse x2+4y2=16 meets the x axis at Q.
If M is the midpoint of the line segment PQ, then the locus of M intersects the latus rectum of the given ellipse at the points
\left(\ \pm3\sqrt{5}/2,\pm2/7 \right)
\left(\ \pm3\sqrt{5}/2,\pm \sqrt{19}/4 \right)
\left(\ \pm2\sqrt{3}, \pm 1/7 \right)
\left(\ \pm2\sqrt{3}, \pm 4\sqrt{3}/7 \right)
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5 Answers
kaymant
·2009-04-12 10:21:41
The answer is C. The locus of M is turning out to be \left(\dfrac{2x}{7}\right)^2+y^2=1.