If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :
JEE · Math · previous-year question
- A.$${{13} \over 6}$$
- B.2
- C.$${{13} \over 12}$$correct
- D.$${{13} \over 8}$$
Answer
C. $${{13} \over 12}$$
Explanation
2b = 5 and 2ae = 13 b2 = a2(e2 $$-$$ 1) $$ \Rightarrow $$ $${{25} \over 4}$$ = $${{169} \over 4}$$ $$-$$ a2 $$ \Rightarrow $$ a $$=$$ 6 $$ \Rightarrow $$ e $$=$$ $${{13} \over {12}}$$
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