Conics Memorization

Focus of an x² parabola

(h, k + c)

Focus of a y² parabola

(h + c, k)

Directrix of an x² parabola

y = k - c

Directrix of a y² parabola

x = h - c

Latus Rectum of a parabola

4c

Equation of an x² parabola

(x - h)² = 4c(y - k)

Equation of a y² parabola

(y - k)² = 4c(x - h)

An x² parabola opens…

Up/down

A y² parabola opens…

Left/right

Equation of a horizontal ellipse

(x - h)² / a² + (y - k)² / b² = 1

Equation of a vertical ellipse

(x - h)² / b² + (y - k)² / a² = 1

Foci of a horizontal ellipse

(h ± c, k)

Foci of a vertical ellipse

(h, k ± c)

Directrices of a horizontal ellipse

x = h ± a²/c

Directrices of a vertical ellipse

y = k ± a²/c

Vertices of a horizontal ellipse

(h ± a, k)

Vertices of a vertical ellipse

(h, k ± a)

Covertices of a horizontal ellipse

(h, k ± b)

Covertices of a vertical ellipse

(h ± b, k)

Latus Rectum of ANY ellipse

(2b²)/a

Eccentricity of ANY ellipse

c/a

A, b, c relation of ANY ellipse

a² = b² + c²

Equation of a left/right hyperbola

(x-h)²/a² - (y-k)²/b² = 1

Equation of an up/down hyperbola

(y-k)²/a² - (x-h)²/b² = 1

Foci of a left/right hyperbola

(h ± c, k)

Foci of an up/down hyperbola

(h, k ± c)

Directrices of a left/right hyperbola

x = h ± a²/c

Directrices of an up/down hyperbola

y = k ± a²/c

Vertices of a left/right hyperbola

(h ± a, k)

Vertices of an up/down hyperbola

(h, k ± a)

Asymptotes of a left/right hyperbola

y - k = ± b/a(x - h)

Asymptotes of an up/down hyperbola

y - k = ± a/b(x - h)

Latus Rectum of ANY hyperbola

(2b²)/a

Eccentricity of ANY hyperbola

c/a

A, b, c relation for ANY hyperbola

c² = a² + b²