First slide

Hyperbola in conic sections

Question

The length of the transverse axis of the rectangular hyperbola xy =18 is

Moderate

A

6
B

12
C

18
D

9

Solution

Transverse axis is along the line y= x.
Solving y = x and xy =18, we have x² =18 or $x = \pm 3 \sqrt{2}$
Then the two vertices of the hyperbola are $(\pm 3 \sqrt{2}, \pm 3 \sqrt{2})$
The distance between them is $\sqrt{72 + 72} = 12$

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