If the distance between the foci and the distance between the directries of the hyperbola x2a2-y2b2-1 are in the ratio 3- 2- then its eccentricity is

For #160;the #160;hyperbola,Distance #160;between #160;fociDistance #160;between #160;directrix=32i.e. #160;2ae2ae=32i.e. #160;e2=32i.e. #160; ...

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If the distance between the foci and the distance between the directries of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ are in the ratio 3:2, then its eccentricity is __________________.

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Solution

$For the hyperbola, \frac{Distance between foci}{Distance between directrix} = \frac{3}{2} i . e . \frac{2 a e}{\frac{2 a}{e}} = \frac{3}{2} i . e . e^{2} = \frac{3}{2} i . e . e = \sqrt{\frac{3}{2}}$

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If the distance between the foci and the distance between the directries of the hyperbola x2a2-y2b2=1 are in the ratio 3:2, then its eccentricity is __________________.

For the hyperbola,Distance between fociDistance between directrix=32i.e. 2ae2ae=32i.e. e2=32i.e. e=32

If the distance between the foci and the distance between the directries of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ are in the ratio 3:2, then its eccentricity is __________________.

$For the hyperbola, \frac{Distance between foci}{Distance between directrix} = \frac{3}{2} i . e . \frac{2 a e}{\frac{2 a}{e}} = \frac{3}{2} i . e . e^{2} = \frac{3}{2} i . e . e = \sqrt{\frac{3}{2}}$