PARABOLAS
G.GPE.2 Derive the equation of a parabola...Also G.GPE.4
Parabolas
A parabola is the set of all points in a plane that are the same distance from a fixed line and a fixed point not on the line. The fixed point is called the focus of a parabola. The fixed line is called the directrix. The distance between the vertex and the focus is the focal length of the parabola.
In this lesson, you will consider vertical parabolas (each of which has a vertical axis of symmetry and a horizontal directrix) and horizontal parabolas (each of which has a horizontal axis of symmetry and vertical directrix). You can find the equation of a vertical parabola with vertex at the origin by using the geometric definition. If you denote the focus by (0,c), the directrix is the line with equation y=-c. Here's why it works: Any point (x,y) on the parabola must be equidistant from the focus and the directrix. Use the Distance Formula.