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The radius of the circle passing throu...

The radius of the circle passing through the foci of the ellipse `(x^(2))/(16) + (y^(2))/( 9) = 1 ` and having its centre at (0,3) is

A

4

B

3

C

`sqrt(12)`

D

`7//2`

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `x^(2)/16 + y^(2)/9 = 1`
The eccentricity e of the ellipse is given by
`e = sqrt(1 - 9/16) = sqrt7/4`
So, the coordinates of the foci are `(pm sqrt7, 0).`
`therefore` Radius of the circle `= sqrt((sqrt7 - 0)^(2) + (0 - 3)^(2)) = 4.`
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