Question

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

• A. $9$
• B. $7$
• C. $11$
• D. $5$

Answer 1

The correct option is C $11$

Equation of ellipse, $\frac{x^2}{{\left(12\right)}^2}+\frac{y^2}{{\left(5\right)}^2}=1$

$e=\sqrt{1-\frac{b^2}{a^2}}$

$e=\sqrt{1-\frac{25}{144}}$

$e=\sqrt{\frac{119}{144}}$

folci of ellipse : $(\pm ae,0)\Rightarrow (\pm \sqrt{119},0)$

Circle have centre, $(0,\sqrt{2})$

Radius = Distance between centre and foci

= $\sqrt{{(\sqrt{119}-0)}^2+{(\sqrt{2}-0)}^2}$

= $\sqrt{121}$

= $11$

Radius = $11$