MathematicsLet P be a point on the ellipse x225+y216=1 with foci S and S1 . Find the maximum area of △SPS1.

Let P be a point on the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$ with foci S and S¹ . Find the maximum area of $△ S P S^{1}$ .

Solution:

$f o r g i v e n e l l i p s e a^{2} = 25, b^{2} = 16 a n d e = \frac{3}{5} Max area = \frac{1}{2} \times 2 a e \times b = a b e = 5 \times 4 \times \frac{3}{5}$

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