Question

Which of the following gives the equation of director circle of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$?

• A. $x^2-y^2=9$
• B. $x^2+y^2=41$
• C. $x^2+y^2=9$
• D. $x^2+y^2=25$

Answer 1

The correct option is B

$x^2+y^2=41$

The equation of director circle of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1is{x}^2+y^2=a^2+b^2$

$\Rightarrow Directorcircleof\frac{x^2}{25}+\frac{y^2}{16}=1is,$

$x^2+y^2=41$