## Hyperbola and right circular cone

Hi,

Given an equation that describes a hyperbola, will this hyperbola be part of a right circular cone (RCC) with a unique aperture or could it be part of RCC's with different apertures?

i.e. given $x^2-2xy-y^2=1$

can I calculate the aperture of the RCC it is a section of?

If this is not possible, is there a certain number of hyperbolae required to be able to calculate the aperture of the RCC.

Thanks