A circle is a locus of points whose distance from a fixed point is a constant. A parabola can also be described as a locus of points whose distance from a fixed point and a fixed line not passing through that point is a constant. An example of a parabola is shown below.

In the figure below, point is called the **focus** of the parabola and line is called its **directrix**. The vertex of the parabola is at the origin O and the -axis the perpendicular bisector of . If we take any point on the parabola, draw , and draw perpendicular to line where Q is line l, then the distance between and and and are equal.

Suppose that the coordinates of the focus is where , then the directrix is (can you see why?).

From here we can see that and . Since is equal to ,

Squaring both sides, we have

.

This is the equation of the parabola with focus and directrix