Circles, Ellipses, Parabolas, and Hyperbola

Vertical Axis (Parabola)

(x-h)^2=4p(y-k)

Vertical Axis (Parabola) Focus

(h, k+p)

Vertical Axis (Parabola) Directrix

y = k - p

Vertical Axis (Parabola) Axis

x = h

Horizontal Axis (Parabola)

(y-k)²=4p(x-h)

Horizontal Axis (Parabola) Focus

(h + p, k)

Horizontal Axis (Parabola) Directrix

x = h - p

Horizontal Axis (Parabola) Axis

y = k

Ellipse: Major Axis (Vertical)

Ellipse: Major Axis (Vertical) Major Vertices

(h, k + a)

(h, k - a)

Ellipse: Major Axis (Vertical) Co-Vertices (Minor)

(h + b, k)

(h - b, k)

Ellipse: Major Axis (Vertical) Foci

(h, k + c)

(h, k - c)

Ellipse: Major Axis (Horizontal)

Ellipse: Major Axis (Horizontal) Major Vertices

(h + a, k)

(h - a, k)

Ellipse: Major Axis (Horizontal) Co-Vertices (Minor)

(h, k + b)

(h, k - b)

Ellipse: Major Axis (Horizontal) Foci

(h + c, k)

(h - c, k)

Horizontal and Vertical Ellipse Distance

c² = a² - b²

Circle

(x-h)² + (y-k)² = r²

Vertical Hyperbola

Vertical Hyperbola Vertices

(h, k + a)

(h, k - a)

Vertical Hyperbola Conjugate Axis (Co-Vertices)

(h + b, k)

(h - b, k)

Vertical Hyperbola Foci

(h, k + c)

(h, k - c)

Vertical Hyperbola Asymptote

y = k ± a/b (x - h)

Horizontal Hyperbola

Horizontal Hyperbola Vertices

(h + a, k)

(h - a, k)

Horizontal Hyperbola Conjugate Axis (Co-Vertices)

(h, k + b)

(h, k - b)

Horizontal Hyperbola Foci

(h + c, k)

(h - c, k)

Horizontal Hyperbola Asymptote

y = k ± b/a (x - h)

Hyperbola Distance

c² = a² + b²

Circle (Graph)

Vertical Parabola

Horizontal Parabola

Vertical Ellipse

Horizontal Ellipse

Vertical Hyperbola (Graph)

Horizontal Hyperbola (Graph)