IntroConics

Parabola

(x−h)² = 4p(y−k)

Overview

A parabola is the set of points equidistant from a focus and a directrix.

Domain

(-∞, +∞)

Range

Depends on orientation

Key Properties

1

Vertex at (h, k)

2

Focus is distance p from vertex

3

Directrix is a line distance p from vertex

4

p > 0 opens up/right, p < 0 opens down/left

Key Insight

The parabola reflects parallel rays to the focus — used in satellite dishes and headlights.

Visualize Parabola

Interact with the graph and explore this curve in the analytic geometry visualizer.

Open Visualizer