Question

Let the equation of an ellipse be $\frac{x^2}{144}+\frac{y^2}{25}=1$. Then, the radius of the circle with centre $(0,\sqrt{2})$ and passing through the foci of the ellipse is :

• A. $9$
• B. $7$
• C. $11$
• D. $5$

Answer 1

The correct option is C $11$

Given equation of ellipse is
$\frac{x^2}{144}+\frac{y^2}{25}=1$
Here, $a^2=144$ and $b^2=25$
Now, $e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{25}{144}}$
$=\sqrt{\frac{119}{144}}=\frac{\sqrt{119}}{12}$
$\therefore$ Foci of an ellipse $=(\pm ae,0)$
$=(\pm 12\times \frac{\sqrt{119}}{12},0)$
$=(\pm \sqrt{119},0)$
Since, the circle with centre $(0,\sqrt{2})$ and passing through foci $(\pm \sqrt{119},0)$ of the ellipse.
$\therefore$ Radius of circle $=\sqrt{{(\sqrt{119}-0)}^2+{(0-\sqrt{2})}^2}$
$=\sqrt{119+2}=\sqrt{121}=11$