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P is a variable on the ellipse (x^2)/...

`P` is a variable on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` with `AA '` as the major axis. Find the maximum area of triangle `A P A '`

A

ab

B

2 ab

C

ab/2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
The maximum area corresponds to when P is at either end of the minor axis and hence for such a position of P, we have
Area of `Delta AP'A = 1/2 (2a) (b) = ab`
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