A) \[16\frac{{{a}^{2}}}{3}\]
B) \[14\frac{{{a}^{2}}}{3}\]
C) \[13\frac{{{a}^{2}}}{3}\]
D) \[16{{a}^{2}}\]
E) \[4{{a}^{2}}\]
Correct Answer: A
Solution :
The equations of given curves are \[{{y}^{2}}=4ax\]and\[{{x}^{2}}=4ay\] On solving these equations, we get (0, 0) and (4a, 4a). \[\therefore \]Required area \[=\int_{0}^{4a}{\left( 2\sqrt{a}\sqrt{x}-\frac{{{x}^{2}}}{4a} \right)}dx\] \[=\left[ 2\sqrt{a}\frac{{{x}^{3/2}}}{3/2}-\frac{{{x}^{3}}}{12a} \right]_{0}^{4a}\] \[=\frac{32}{3}{{a}^{2}}-\frac{16{{a}^{2}}}{3}\] \[=\frac{16{{a}^{2}}}{3}sq\,unit\]
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