center

Definition of circle
The locus of point that moves such that its distance from a fixed point called the center is constant. The constant distance is called the radius, r of the circle.
 

Definition

Hyperbola can be defined as the locus of point that moves such that the difference of its distances from two fixed points called the foci is constant. The constant difference is the length of the transverse axis, 2a.
 

Elements of the ellipse are shown in the figure below.
 

Definition of Ellipse
Ellipse is the locus of point that moves such that the sum of its distances from two fixed points called the foci is constant. The constant sum is the length of the major axis, 2a.