Parabola Explained: Step-by-Step Calculus Notes with Examples, Practice Problems, and Clear Graphing Explanations

MASTERING THE PARABOLA
Ultimate Exam Cheat Sheet & Concise Notes


A parabola is the locus of a point which moves such that its distance from a fixed point
(Focus) is always equal to its distance from a fixed straight line (Directrix).


1. Standard Equations and Variants



Feature y² = 4ax y² = -4ax x² = 4ay x² = -4ay

Focus (a, 0) (-a, 0) (0, a) (0, -a)

Directrix x = -a x=a y = -a y=a

Vertex (0, 0) (0, 0) (0, 0) (0, 0)

Axis y=0 y=0 x=0 x=0

Latus Rectum 4a 4a 4a 4a