We have four conic sections, each with their own distinct foci relationships. The locus of points to foci for a hyperbola all have the same difference between the two foci. What this means is that the difference between the distances of any point on the hyperbola and the two foci will be the same. For a parabola the distance between a point and the foci is the same as the distance between that point and the directrix. For an ellipse, the sum of the distances between any point and the foci are congruent. For a circle all points are equidistant to the center, the focus. This is basically just defining a radius, a familiar concept, but treating the center as a focus!
Click on the links provided for a visual display of each conic section and a proof of their relationship with their foci!
Click on the links provided for a visual display of each conic section and a proof of their relationship with their foci!