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

Answer: (A)

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 $=\sqrt{{(0-\sqrt{7})}^2+{(3-0)}^2}=4$