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

English

Gujarati

Hindi

10-2. Parabola, Ellipse, Hyperbola

normal

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

Share

Similar Questions

If the eccentricity of the standard hyperbola passing, through the point $(4, 6)$ is $2$, then the equation of the tangent to the hyperbola at $(4, 6)$ is

hard

(JEE MAIN-2019)

An ellipse intersects the hyperbola $2 x^2-2 y^2=1$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then

$(A)$ Equation of ellipse is $x^2+2 y^2=2$

$(B)$ The foci of ellipse are $( \pm 1,0)$

$(C)$ Equation of ellipse is $x^2+2 y^2=4$

$(D)$ The foci of ellipse are $( \pm \sqrt{2}, 0)$

hard

(IIT-2009)

Eccentricity of the curve ${x^2} – {y^2} = {a^2}$ is

normal

A hyperbola having the transverse axis of length $\sqrt{2}$ has the same foci as that of the ellipse $3 x^{2}+4 y^{2}=12,$ then this hyperbola does not pass through which of the following points?

hard

(JEE MAIN-2020)

The equation of the tangent to the hyperbola $2{x^2} – 3{y^2} = 6$ which is parallel to the line $y = 3x + 4$, is

easy