The Circle

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.
 

The Parabola

Definition of Parabola

Parabola is the locus of point that moves such that it is always equidistant from a fixed point and a fixed line. The fixed point is called focus and the fixed line is called directrix.
 

Parabola with vertex at the origin and open to the right

 

The Hyperbola

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 Hyperbola

 

The Ellipse

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.
 

Ellipse and all its elements