Question

The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ and having its centre $(0,3)$, is?

• A. $4$
• B. $3$
• C. $\sqrt{12}$
• D. $7/2$

Answer 1

The correct option is A $4$

Let $e$ be the eccentricity of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$
Then, $e=\sqrt{1-\frac{9}{16}}=\frac{\sqrt{7}}{4}$
So, coordinates of the foci of the ellipse are $(\pm \sqrt{7},0)$.
The radius of the circle having centre at $(0,3)$ and passing through foci
$=\sqrt{(0-\sqrt{7}{)}^2+(3-0{)}^2}=4$.