In a hyperbola,if the length of the transverse axis is twice that of the conjugate axis,then the distance between its directrices is..... units.

The equation of the pair of asymptotes of the hyperbola $\frac{(x-3)^2}{3}-\frac{(y-2)^2}{2}=1$ is

What will be the equation of the chord of the hyperbola $25x^2 - 16y^2 = 400$,whose midpoint is $(5, 3)$?

If the distance between the foci of a hyperbola $H$ is $26$ and the distance between its directrices is $\frac{50}{13}$,then the eccentricity of the conjugate hyperbola of the hyperbola $H$ is

The locus of the point of intersection of any two perpendicular tangents to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is a circle,which is called the director circle of the hyperbola. What is the equation of this circle?

Let a line $L_{1}$ be tangent to the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{4}=1$ and let $L_{2}$ be the line passing through the origin and perpendicular to $L_{1}$. If the locus of the point of intersection of $L_{1}$ and $L_{2}$ is $(x^{2}+y^{2})^{2} = \alpha x^{2}+\beta y^{2}$,then $\alpha+\beta$ is equal to