Question

The area of the director circle of the ellipse $\frac{x^2}{5}+\frac{y^2}{4}=1$ is

• A. $5\pi \text{sq. units}$
• B. $4\pi \text{sq. units}$
• C. $9\pi \text{sq. units}$
• D. $18\pi \text{sq. units}$

Answer 1

The correct option is C $9\pi \text{sq. units}$

Given : $\frac{x^2}{5}+\frac{y^2}{4}=1$
We know, equation of director circle of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $x^2+y^2=a^2+b^2$

Here,$a^2=5,b^2=4$
$\therefore$ Equation of director circle is
$x^2+y^2=5+4\Rightarrow x^2+y^2=9=r^2\therefore \text{Area}=\pi r^2=9\pi \text{sq. units}$