Core Concepts · Parabola Quick Reference
A parabola is the locus of points equidistant from a fixed point (focus) and a fixed line (directrix).
Standard Forms
Standard Forms
y² = 4px (opens right)
y² = -4px (opens left)
x² = 4py (opens up)
x² = -4py (opens down)
Key relationships:
Focus:
Latus rectum length =
Translated form:
Focus:
(p, 0) | Directrix: x = -p | Vertex: (0, 0)Latus rectum length =
|4p| | Axis of symmetry along the axis of the parabolaTranslated form:
(y-k)² = 4p(x-h) or (x-h)² = 4p(y-k), vertex at (h,k)
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