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What is the area enclosed by the curve $2 \mathrm{x}^{2}+\mathrm{y}^{2}=1$ ?
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Verified Answer
The correct answer is:
$\frac{\pi}{\sqrt{2}} \quad$
Given equation of curve $2 x^{2}+y^{2}=1$ is an ellipse which can be written as $\frac{x^{2}}{y^{2}}+\frac{y^{2}}{1}=1$
Area of ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ is $A=\pi$ ab sq unit
Here, $\mathrm{a}=\frac{1}{\sqrt{2}}, \mathrm{~b}=1$.
: Required area $=\pi \cdot \frac{1}{\sqrt{2}} \cdot 1=\frac{\pi}{\sqrt{2}}$ sq unit
Area of ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ is $A=\pi$ ab sq unit
Here, $\mathrm{a}=\frac{1}{\sqrt{2}}, \mathrm{~b}=1$.
: Required area $=\pi \cdot \frac{1}{\sqrt{2}} \cdot 1=\frac{\pi}{\sqrt{2}}$ sq unit
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