Circles, ellipses and hyperbolae have similar equations: All these curves are obtained from the intersection of a plane with a cone as shown above.
for a circle of ellipses centred at the origin, with
for a circle and
for an ellipse and
for a circle or ellipse centred at
For a hyperbola,
centred at the origin or
for a hyperbola centred atat with again
are all equations of parabolae.