Question

Equation of director circle of the ellipse $\frac{x^2}{3}+\frac{y^2}{6}=1$ is

• A. $x^2+y^2=36$
• B. $x^2+y^2=9$
• C. $x^2+y^2=45$
• D. $x^2+y^2=81$

Answer 1

The correct option is B $x^2+y^2=9$

Given : $\frac{x^2}{3}+\frac{y^2}{6}=1$
We know that, equation of director circle of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $x^2+y^2=a^2+b^2$
Here, $a^2=3,b^2=6$
$\therefore$ Equation of director circle is $x^2+y^2=9$