Question

The equation of the circle passing through the foci of the ellipes ${\frac{x}{16}}^2+{\frac{y}{9^{}}}^2=1$ and having centre at $\left(0,3\right)$ 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 $x^2+y^2-6y-7=0$

R.E.F image

Equation of ellipse : $\frac{x^2}{16}+\frac{y^2}{9}=1$

coordinate of foci are $(ac,o);(-ac,o)$

$e=\sqrt{1-\frac{9}{16}}=\frac{\sqrt{7}}{4}$

$a=4$

co-ordinate of foci $=(\sqrt{7},0),(-\sqrt{7},0)$

$R=\sqrt{7+9}=4$

$(x-0{)}^2+(y-3{)}^2=4^2$

$x^2+y^2-6y+9=16$

$x^2+y^2-6y-7=0$