The distance between the directrices of a rectangular hyperbola is $10$ units. What is the distance between its foci?

If the eccentricity of a hyperbola is $\frac{5}{3}$,then the eccentricity of its conjugate hyperbola is

The eccentricity of the hyperbola conjugate to ${x^2} - 3{y^2} = 2x + 8$ is

The locus of the point of intersection of the lines $ax \sec \theta + by \tan \theta = a$ and $ax \tan \theta + by \sec \theta = b$,where $\theta$ is the parameter,is

The curve $xy = c^2$ is known as:

The locus of the feet of the perpendiculars drawn from either focus onto a variable tangent to the hyperbola $16y^2 - 9x^2 = 1$ is