A) \[4{{x}^{2}}-5{{y}^{2}}=100\]
B) \[5{{x}^{2}}-4{{y}^{2}}=100\]
C) \[4{{x}^{2}}+5{{y}^{2}}=100\]
D) \[5{{x}^{2}}+4{{y}^{2}}=100\]
Correct Answer: A
Solution :
\[\frac{2{{b}^{2}}}{a}=8\] and \[\frac{3}{\sqrt{5}}=\sqrt{1+\frac{{{b}^{2}}}{{{a}^{2}}}}\] or \[\frac{4}{5}=\frac{{{b}^{2}}}{{{a}^{2}}}\] Þ \[a=5\], \[b=2\sqrt{5}\]. Hence the required equation of hyperbola is \[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{20}=1\] Þ \[4{{x}^{2}}-5{{y}^{2}}=100\].
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