Question

Area bounded by the ellipse $4x^2+9y^2=1$ is _____

• A. $\frac{\pi }{36}$
• B. $6\pi$
• C. $36\pi$
• D. $\frac{\pi }{6}$

Answer 1

The correct option is A $\frac{\pi }{36}$

$4x^2+9y^2=1=\frac{x^2}{\frac{1}{4}}+\frac{y^2}{\frac{1}{9}}=1$

General form of equation of an ellipse is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Also the area$=\pi ab$

Here $a=\frac{1}{4},b=\frac{1}{9}$

Area of this ellipse$=\pi \times \frac{1}{4}\times \frac{1}{9}=\pi \times \frac{1}{36}=\frac{\pi }{36}$