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.