question_answer

If the centre, vertex and focus of a hyperbola be (0, 0), (4, 0) and (6, 0) respectively, then the equation of the hyperbola is

A)            \[4{{x}^{2}}-5{{y}^{2}}=8\]       

B)            \[4{{x}^{2}}-5{{y}^{2}}=80\]

C)            \[5{{x}^{2}}-4{{y}^{2}}=80\]     

D)            \[5{{x}^{2}}-4{{y}^{2}}=8\]

Correct Answer: C

Solution :

                   Centre (0, 0), vertex (4, 0) Þ and focus                      Þ \[ae=4\]Þ \[e=\frac{3}{2}\]. Therefore \[b=\]                    Hence required equation is \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{20}=1\]                    i.e., \[5{{x}^{2}}-4{{y}^{2}}=80\].