A) 8
B) 4
C) 3
D) 7
E) 12
Correct Answer: A
Solution :
Equation of given conic is \[7{{x}^{2}}-9{{y}^{2}}=63\] \[\Rightarrow \] \[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{7}=1\] Comparing it with hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[\Rightarrow \] \[a=3,b=\sqrt{7}\] \[\Rightarrow \] \[a>b\] \[\Rightarrow \] \[e=\sqrt{1+\frac{{{b}^{2}}}{{{a}^{2}}}}\] \[=\sqrt{1+\frac{7}{9}}=\frac{4}{3}\] \[\therefore \]Foci = (4, 0) and \[(-4,0)\] \[\therefore \]Required distance\[=\sqrt{{{(4+4)}^{2}}}=8\]
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