If for a hyperbola ratio of length of conjugate Axis to length of transverse axis is 3 : 2 the

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10-2. Parabola, Ellipse, Hyperbola

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If for a hyperbola the ratio of length of conjugate Axis to the length of transverse axis is $3 : 2$ then the ratio of distance between the focii to the distance between the two directrices is

A

$13 : 4$

B

$4 : 13$

C

$\sqrt {13} :2$

D

$2:\sqrt {13} $

Solution

$\frac{b}{a}=\frac{3}{2},$

Now $\frac{2 a e}{\frac{2 a}{e}}=e^{2}=1+\frac{b^{2}}{a^{2}}$

$=1+\frac{9}{4}=\frac{13}{4}$

Standard 11

Mathematics

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