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; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Quantitative Aptitude

Length Based Approach

If the distan...

Question

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 __________________.

Open in App

Solution

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

Suggest Corrections

Similar questions

Q. If the distance between the foci and the distance between the two directricies of a hyperbola are in the ratio

5 : 4

, then the eccentricity of the hyperbola is :

In a hyperbola the distance between the foci is 2 and the distance between directrices is 1 Its eccentricity is

If the eccentricities of the hyperbolas $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 a n d \frac{y^{2}}{b^{2}} - \frac{x^{2}}{a^{2}} = 1$ be e and $e_{1}$ , then $\frac{1}{e^{2}} + \frac{1}{e_{1}^{2}} =$

Q. If the distance between the foci of a hyperbola is 16 and its eccentricity is

\sqrt{2}

, then obtain the equation of the hyperbola.

If the eccentricity of a hyperbola is $\sqrt{2}$ and if the distance between the foci is 16, then its equation is

Join BYJU'S Learning Program

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 __________________.

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