A) \[25{{x}^{2}}-144{{y}^{2}}=900\]
B) \[144{{x}^{2}}-25{{y}^{2}}=900\]
C) \[144{{x}^{2}}+25{{y}^{2}}=900\]
D) \[25{{x}^{2}}+144{{y}^{2}}=900\]
Correct Answer: A
Solution :
Conjugate axis is 5 and distance between foci = 13 Þ \[2b=5\]and\[2ae=13\]. Now, also we know for hyperbola \[{{b}^{2}}={{a}^{2}}({{e}^{2}}-1)\] Þ \[\frac{25}{4}=\frac{{{(13)}^{2}}}{4{{e}^{2}}}({{e}^{2}}-1)\] Þ \[\frac{25}{4}=\frac{169}{4}-\frac{169}{4{{e}^{2}}}\] or \[{{e}^{2}}=\frac{169}{144}\] Þ \[e=\frac{13}{12}\] or \[a=6,\,b=\frac{5}{2}\] or hyperbola is \[\frac{{{x}^{2}}}{36}-\frac{{{y}^{2}}}{25/4}=1\] Þ \[25{{x}^{2}}-144{{y}^{2}}=900\].
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