A) \[\pi \] sq unit
B) \[2\] sq unit
C) \[3\pi \] sq unit
D) \[4\]sq unit
Correct Answer: D
Solution :
The given equation can be rewritten as \[\frac{{{(x-\sqrt{2})}^{2}}}{2/\pi }+\frac{{{y}^{2}}}{8/\pi }=1\] Which represents an ellipse. Here, \[a=\sqrt{\frac{2}{\pi }}\] and \[b=\sqrt{\frac{8}{\pi }}\] Area enclosed in an ellipse\[=\pi ab\] \[=\pi \sqrt{\frac{2}{\pi }}\sqrt{\frac{8}{\pi }}=\sqrt{16}\] \[=4\,\text{sq}\text{.}\,\text{unit}\]
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