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P is a variable point on the ellipse x^2...

`P` is a variable point on the ellipse `x^2/a^2+y^2/b^2=2\ (a gt b)` whose foci are `F_1` and `F_2`. The maximum area (in `unit^2)`of the `Delta PFF'` is

A

`2asqrt(a^(2)-b^(2))`

B

`2bsqrt(a^(2)-b^(2))`

C

`asqrt((2a^(2)-2b^(2)))`

D

`bsqrt((2a^(2)-2b^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
B

area of `DeltaPF_(1)F_(2)=A=1/2(2sqrt(2)ae)sqrt(2)bsintheta`
`impliesA=2abesintheta`
`=(2ab)/a sqrt(a^(2)-b^(2))=2bsqrt(a^(2)-b^(2))`
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