Question

Area of region enclosed by ellipse $x^2+4y^2=1$ is ______

• A. $\frac{\pi }{2}$
• B. $\pi$
• C. $2\pi$
• D. $4\pi$

Answer 1

The correct option is A $\frac{\pi }{2}$

$x^2+4y^2=1$
$\therefore$ From, $\frac{x^2}{1}+\frac{y^2}{1}=1,a^2=1,b^2=\frac{1}{2}$
$\therefore a=1,b=\frac{1}{2}$
Now as per the illustration
area of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ (where $a>b$) is $\pi ab$
$\therefore$ Required area is $\pi \left(1\right)\left(\frac{1}{2}\right)$
$\therefore$ Area$=\frac{\pi }{2}$