If the eccentricity $e$ of a conic satisfies the equation $2e^3 + 10e - 13 = 0$,then that conic is

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

If the line $lx + my = 1$ is a normal to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,then $\frac{a^2}{l^2} - \frac{b^2}{m^2}$ is equal to

Let the ellipse $E: \frac{x^{2}}{144}+\frac{y^{2}}{169}=1$ and the hyperbola $H: \frac{x^{2}}{16}-\frac{y^{2}}{\lambda^{2}}=-1$ have the same foci. If $e$ and $L$ respectively denote the eccentricity and the length of the latus rectum of $H$, then the value of $24(e+L)$ is:

Find the equation of the hyperbola satisfying the given conditions: Vertices $(\pm 7, 0)$,$e = \frac{4}{3}$.

The centre of the hyperbola $9x^{2} - 36x - 16y^{2} + 96y - 252 = 0$ is: