A _______ is the set of all points in a plane, the difference of whose distances from two fixed points in a plane is constant.
Dear student, A hyperbola is "the set of all points in a plane such that the difference of the distances from two fixed points (foci) is constant". The difference of the distances to any point on the hyperbola (x,y) from the two foci (c,0) and (-c,0) is a constant. That constant will be 2a. Regards.