A parabola is the locus of points defined by the condition that the the distance from a point on the curve to a fixed point F is equal to the least distance from that point on the line to a fixed line L:
The point F is called the focus.
The point L is called the directrix.
If the points
have coordinates
respectively then the distance
and
This equation of for a vertex at the origin If the vertex is at the point
and the curve oriented above then
In general the parabola may be scaled, translated and rotated. The most general equation of an parabola is
with the condition that