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

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

If the area of the quadrilateral formed by the tangents drawn at the ends of the latus rectum of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is equal to the square of the distance between the center and one focus of the hyperbola,then $e^3$ is ($e$ is the eccentricity of the hyperbola).

The equation of the hyperbola whose conjugate axis is $5$ and the distance between the foci is $13$,is

If the vertices and foci of a hyperbola are respectively $(\pm 3,0)$ and $(\pm 4,0)$,then the parametric equations of that hyperbola are:

If the eccentricity of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,passing through $(6, 4\sqrt{3})$,satisfies $15(e^2 + 1) = 34e$,then the length of the latus rectum of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{2(a^2 + 1)} = 1$ is: