The equations of two cones are given;
$(x-x_{0})^2+(y-y_{0})^2=\frac {(z-z_{0})^2}{m^2}$
and
$(x-x_{1})^2+(y-y_{1})^2=\frac {(z-z_{1})^2}{m^2}$
How to find the equations of intersections
1) When the intersection is an ellipse?
2) When the intersection is a hyperbola?