## The Parabola

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 pointshave coordinatesrespectively then the distance and

This equation of for a vertex at the origin If the vertex is at the pointand the curve oriented above thenIn general the parabola may be scaled, translated and rotated. The most general equation of an parabola iswith the condition that