# Parabola

## Definition

A parabola is the set of all points where each point is equidistant to a fixed point, the focus, and to a fixed line, the directrix.

## Equations

- Form of equation { y=a(x-h)² + k { x=a(y-k)² + h
- Direction of opening { upward if a > 0 , Downward if a<0 { Right is a>0,left if a<0
- Vertex { (h,k) { (h,k)
- Axis of symmetry { (h,k + 1/4a) { (h + 1/4a,k)
- Focus { (h,k+1/4a) { (h+1/4a,k)
- Directrix { y=k-1/4a { x=h-1/4a
- Length of latus rectum { |1/a| units { |1/a| units