JEE PYQ: Hyperbola Question 17
Question 17 - 2019 (09 Jan Shift 2)
A hyperbola has its centre at the origin, passes through the point $(4, 2)$ and has transverse axis of length 4 along the $x$-axis. Then the eccentricity of the hyperbola is:
(1) $\frac{3}{2}$
(2) $\sqrt{3}$
(3) 2
(4) $\frac{2}{\sqrt{3}}$
Show Answer
Answer: (4)
Solution
$2a = 4$, $a = 2$. $\frac{x^2}{4} - \frac{y^2}{b^2} = 1$. Passes through $(4, 2)$: $4 - \frac{4}{b^2} = 1$, $b^2 = \frac{4}{3}$. $e = \sqrt{1 + \frac{b^2}{a^2}} = \sqrt{1 + \frac{1}{3}} = \frac{2}{\sqrt{3}}$.
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