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If normal at any point P to the ellipse `x^2/a^2+y^2/b^2=1(a > b)` meets the axes at A and B such that `PA:PB = 1:2,` then the equation of the director circle of the ellipse is

A

`x ^(2) +y ^(2) = (a ^(2))/(2)`

B

`x ^(2) +y ^(2)= (3a ^(2))/(2)`

C

`x^(2) +y ^(2) =(2a ^(2))/(3)`

D

`x ^(2) +y ^(2) = (a ^(2))/(3)`

Text Solution

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The correct Answer is:
B
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