First slide

Hyperbola in conic sections

Question

If the distance between two directrices of a rectangular hyperbola is 15, then the distance between its foci in units is:

Moderate

A

$15 \sqrt{2}$
B

30
C

60
D

45

Solution

We know that the eccentricity of a rectangular hyperbola is $e = \sqrt{2}$
Distance between the directricess $= {\frac{2 a}{e}}^{},$
where $2 a$ is the length of the transverse axis.
So $\frac{2 a}{e} = 15 \Rightarrow 2 a = 15 \sqrt{2}$
Distance between the foci $= 2 a e = 15 \sqrt{2} \times \sqrt{2} = 30 .$

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