For the ellipse with foci and

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

For the ellipse x216+y29=1\dfrac{x^{2}}{16}+\dfrac{y^{2}}{9}=1 with foci S1(−7,0)S_{1}(-\sqrt7,0) and S2(7,0)S_{2}(\sqrt7,0), let P(t, 3416−t2)P(t,\,\tfrac{3}{4}\sqrt{16-t^{2}}) be any point on the ellipse (∣t∣≤4|t|\le 4). Show that PS1+PS2=8PS_{1}+PS_{2}=8.

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