A) \[3{{x}^{2}}-5{{y}^{2}}=25\]
B) \[5{{x}^{2}}-3{{y}^{2}}=225\]
C) \[25{{x}^{2}}-9{{y}^{2}}=225\]
D) \[9{{x}^{2}}-25{{y}^{2}}=225\]
Correct Answer: D
Solution :
The given equation of asymptotes of hyperbola is \[3x\pm 5y=0\] ...(i) and vertices \[(\pm 5,0)\] Now, equation of hyperbola is \[(3x+5y)\,(3x-5y)=\lambda \] \[9{{x}^{2}}-25{{y}^{2}}=\lambda \] ...(ii) Since, \[(\pm \,5,0)\] is the vertices of the hyperbola, then \[9{{(5)}^{2}}-0-\lambda \Rightarrow \lambda =225\] From Eq. (ii), \[9{{x}^{2}}-25{{y}^{2}}=225\]
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