Let P is any point on ellipse frac{{{x^2}}}{{{a^2}}} + frac{{{y^2}}}{{{b^2}}} = 1 . S₁ and S₂ it

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10-2. Parabola, Ellipse, Hyperbola

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Let $P$ is any point on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ . $S_1$ and $S_2$ its foci then maximum area of $\Delta PS_1S_2$ is (in square units)

A

$b^2e$

B

$a^2e$

C

$ab$

D

$abe$

Solution

$\Delta=\frac{1}{2}(2 a e)(b \sin \theta)$

Maximum when $\sin \theta=1$

$\Delta= abe$

Standard 11

Mathematics

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