A) \[5{{x}^{2}}-9{{y}^{2}}=180\]
B) \[9{{x}^{2}}+5{{y}^{2}}=180\]
C) \[{{x}^{2}}+9{{y}^{2}}=180\]
D) \[5{{x}^{2}}+9{{y}^{2}}=180\]
Correct Answer: D
Solution :
\[2ae=8,\,\,\frac{2a}{e}=18\]Þ \[a=\sqrt{4\times 9}=6\] \[e=\frac{2}{3},\]\[b=6\sqrt{1-\frac{4}{9}}=\frac{6}{3}\sqrt{5}=2\sqrt{5}\] Hence the required equation is \[\frac{{{x}^{2}}}{36}+\frac{{{y}^{2}}}{20}=1\] i.e., \[5{{x}^{2}}+9{{y}^{2}}=180\].
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