First slide

Hyperbola in conic sections

Question

$Length of the latus rectum of the hyperbola x y = c^{2} is equal to$

Moderate

A

$2 c$
B

$\sqrt{2} c$
C

$2 \sqrt{2} c$
D

$4 c$

Solution

$Length of latus rectum = \frac{2 b^{2}}{a}$
$\begin{array}{l} For x y = c^{2}, a = b and \frac{a^{2}}{2} = c^{2} \\ Required length = 2 \cdot \frac{a^{2}}{a} = 2 a = 2 \sqrt{2} c \end{array}$

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