If a hyperbola has length of its conjugate axis is equal to 5 and distance between foci is 13

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Solution

Q.
If a hyperbola has length of its conjugate axis is equal to 5 and distance between foci is 13. Then eccentricity of the hyperbola is _____

1 $\frac{13}{12}$

2 $2$

3 $\frac{13}{6}$

4 $\frac{13}{8}$

Ans.
(1)

$2 b = 5,$ $2 a e = 13,$ $4 b^{2} = 25,$ $4 (a^{2} e^{2} - a^{2}) = 25$

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