The normal at a point on the ellipse meets the -axis at

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

The normal at a point PP on the ellipse x2+4y2=16x^2 + 4y^2 = 16 meets the XX -axis at QQ . If MM is the mid-point of the line segment PQPQ , then the locus of MM intersects the latusrectum of the given ellipse at the points (1) (±352,±27)\left( \pm \frac{3\sqrt{5}}{2}, \pm \frac{2}{7} \right) (2) (±352,±194)\left( \pm \frac{3\sqrt{5}}{2}, \pm \sqrt{\frac{19}{4}} \right) (3) (±23,±17)\left( \pm 2\sqrt{3}, \pm \frac{1}{7} \right) (4) (±23,±437)\left( \pm 2\sqrt{3}, \pm \frac{4\sqrt{3}}{7} \right)

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