Question

The radius of the circle passing through the foci of the ellipse $9x^2+16y^2=144$ and having its centre at $(0,3),$ is:

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

Answer 1

The correct option is A $4$

Given ellipse is $\frac{x^2}{16}+\frac{y^2}{9}=1$

$a=4,b=3$

$e^2=1-\frac{b^2}{a^2}=1-\frac{9}{16}=\frac{7}{16}\Rightarrow e=\frac{\sqrt{7}}{4}$

Foci of ellipse is $(\pm ae,)$

$\Rightarrow$ Foci is $(\pm \sqrt{7},0)$

Center of the circle is $(0,3),$

Radius is the distance between the foci and centre of circle

$\Rightarrow r=\sqrt{{(\pm \sqrt{7}-0)}^2+{(0-3)}^2}=\sqrt{16}=4$

Hence, option $A$ is correct.