JEE PYQ: Hyperbola Question 20
Question 20 - 2019 (11 Jan Shift 2)
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:
(1) $\frac{13}{12}$
(2) 2
(3) $\frac{13}{6}$
(4) $\frac{13}{8}$
Show Answer
Answer: (1)
Solution
$2b = 5$, $2ae = 13$. $b^2 = a^2(e^2 - 1)$, so $\frac{25}{4} = a^2e^2 - a^2 = \frac{169}{4} - a^2$. Hence $a^2 = 36$, $a = 6$. $ae = \frac{13}{2}$, so $e = \frac{13}{12}$.
BETA
