The tangents to an ellipse and a homofocal hyperbola at each one of their intersection points P are perpendicular. The circle through the point P and the common focal points F_{1}, F_{2} passes also through the intersection points Q_{1}, Q_{2} of the tangents with the minor axis.

The two conics, considering their geometric definition as loci having constant sum/difference of distances from the two foci (F_{1}, F_{2} common to the two conics), have their tangents coincide with the exterior/interior bisector of angle F_{1}PF_{2} (see Ellipse.html ).