P is a variable point on ellipse frac{{{x^2}}}{{{a^2}}} + frac{{{y^2}}}{{{b^2}}} = 1 wit

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10-2. Parabola, Ellipse, Hyperbola

normal

$P$ is a variable point on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ with $AA'$ as the major axis. Then the maximum value of the area of $\Delta APA'$ is

$\left| {ab} \right|$

$\left| {\frac{{ab}}{2}} \right|$

$\left| {2ab} \right|$

$\left| {\frac{{ab}}{4}} \right|$

Maximum area corresponds to when $P$ is at either end of the minor exis and hence area for such position of $P = \frac{1}{2}2ab = ab$

Standard 11

Mathematics

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(JEE MAIN-2021)