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Conic Sections Explorer
AP Precalculus · Analytic Geometry
Learning Objectives
Identify circle, ellipse, parabola, hyperbola
Understand foci, vertices, directrix
Eccentricity determines shape
Standard form equations
Eccentricity e
Circle: e = 0
Ellipse: 0 < e < 1
Parabola: e = 1
Hyperbola: e > 1

e = c/a (ellipse/hyperbola)
c² = a² − b² (ellipse)
c² = a² + b² (hyperbola)
Tags
conic sectionseccentricityellipseparabolahyperbola
CONIC TYPE
a (semi-major) 3.0
b (semi-minor) 2.0
x²/9 + y²/4 = 1
Eccentricity e
—
Focal Distance c
—
Center
(0, 0)
Vertices
—
Red dots: Foci
Green dots: Vertices
Amber dashed: Directrix (parabola)