Question

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

• A. $x^2+y^2-6y-7=0$
• B. $x^2+y^2-6y+7=0$
• C. $x^2+y^2-6y-5=0$
• D. $x^2+y^2-6y+5=0$

Answer 1

The correct option is A $x^2+y^2-6y-7=0$

The equation of the ellipse is
$\frac{x^2}{16}+\frac{y^2}{9}=1$
So, $c=\pm \sqrt{a^2-b^2}$
$=\sqrt{16-9}$
$\Rightarrow c=\pm \sqrt{7}$

radius of circle, $r=O{F}^{\prime }$
$=\sqrt{(3-0{)}^2+(0-\sqrt{7}{)}^2}$
$=4$
Equation of circle having centre $(0,3)$ and radius $4$ is
$(x-0{)}^2+(y-3{)}^2=4^2$
$\Rightarrow x^2+y^2-6y-7=0$