Area bounded by the ellipse 2 x^2+3 y^2-1 is - Vidyadip

MCQ

Area bounded by the ellipse $2 x^2+3 y^2-1$ is

A
$\frac{\pi}{6}$
✓
$\frac{\pi}{\sqrt{6}}$
C
$6 \pi$
D
$\sqrt{6} \pi$

✓

Answer

Correct option: B.

$\frac{\pi}{\sqrt{6}}$

(B)
$2 x^2+3 y^2=1$
$\Rightarrow \frac{x^2}{\left(\frac{1}{\sqrt{2}}\right)^2}+\frac{y^2}{\left(\frac{1}{\sqrt{3}}\right)^2}=1$
Here, $a=\frac{1}{\sqrt{2}}$ and $b=\frac{1}{\sqrt{3}}$
$\therefore \text {Required area }=\pi \times \frac{1}{\sqrt{2}} \times \frac{1}{\sqrt{3}}$
Area of ellipse $\frac{x^2}{ a ^2}+\frac{y^2}{b^2}=1$ is $\pi ab$ sq. units.
.(=\frac{\pi}{\sqrt{6}}$

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