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Standard XI

Mathematics

Standard Form of an Ellipse

P is a variab...

Question

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 $△ A P A^{'}$ is

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2ab

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Solution

The correct option is A ab
The triangle APA’ has maximum area when P coincides with B (end point of minor axis).
$∴$ Maximum area of $△ A P A^{'}$ is OB = $\frac{1}{2}$ 2a.b = ab

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P is a variable point on the ellipse x2a2+y2b2=1 with AA’ as the major axis. Then the maximum value of the area of △APA′ is

The correct option is A abThe triangle APA’ has maximum area when P coincides with B (end point of minor axis). ∴ Maximum area of △APA′ is OB = 12 2a.b = ab

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 $△ A P A^{'}$ is

The correct option is A ab
The triangle APA’ has maximum area when P coincides with B (end point of minor axis).
$∴$ Maximum area of $△ A P A^{'}$ is OB = $\frac{1}{2}$ 2a.b = ab