Conic Sections — Circles and Parabolas

(x-h)²+(y-k)²=r²

Circle equation

(x-h)²=4p(y-k)

Vertical parabola

(y-k)²=4p(x-h)

Horizontal parabola

P

The distance from the vertex to the focus

Vertex

The midpoint between the focus and the directrix

Axis of symmetry

The line passing through the focus and the vertex

Always perpendicular

The directrix and the axis of symmetry are…

Focal width

A line segment perpendicular to the axis of symmetry that passes through the focus and has endpoints on the parabola

Parabola

This conic equation has 1 squared term

Circle

This conic equation has 2 squared terms

Pi(r²)

Area formula (circle)

2(pi)r

Circumference formula