A) \[3{{x}^{2}}+5{{y}^{2}}=32\]
B) \[3{{x}^{2}}+5{{y}^{2}}=25\]
C) \[3{{x}^{2}}+{{y}^{2}}=4\]
D) \[3{{x}^{2}}+{{y}^{2}}=9\]
Correct Answer: A
Solution :
Let the equation of ellipse be \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[\because \] It passes through (? 3, 1) So \[\frac{9}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=1\Rightarrow 9+\frac{{{a}^{2}}}{{{b}^{2}}}={{a}^{2}}\] .....(i) Given eccentricity is \[\sqrt{2/5}\] So \[\frac{2}{5}=1-\frac{{{b}^{2}}}{{{a}^{2}}}\Rightarrow \frac{{{b}^{2}}}{{{a}^{2}}}=\frac{3}{5}\] .....(ii) From equation (i) and (ii), \[{{a}^{2}}=\frac{32}{3},{{b}^{2}}=\frac{32}{5}\] Hence required equation of ellipse is \[3{{x}^{2}}+5{{y}^{2}}=32\].
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