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Find the co-ordinates of all the points P on the ellipse, `x^2/a^2+y^2/b^2=1` ,for which the area of the triangle PON is maximum, where O denotes the origin and N, the foot of the perpendicular from O to tangent at P.

A

`((4)/(sqrt(5)),(1)/(sqrt(5)))`

B

`(-(4)/(sqrt(5)),(1)/(sqrt(5)))`

C

`((1)/(sqrt(5)),(4)/(sqrt(5)))`

D

`((41)/(sqrt(5))-(4)/(sqrt(5)))`

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The correct Answer is:
A, B
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