conics sections

Circle

Has x² and y² , same signs , same coefficient

Ellipse

Equals 1, x² and y² , same signs, different coefficients

Hyperbola

Equals 1, x² and y² , opposite signs

Parabola

Only has x² or y²

Horizontal major axis

x²/a² + y²/b² = 1

Vertical Major Axis

x²/b² + y²/a²

Focus equation for Ellipse

c² = a² - b²

Major axis

2a

Minor axis

2b

Location of a² in hyperbolas

Under positive term

Horizontal transverse axis

x²/a² - y²/b² = 1

Asymptotes of a horizontal hyperbola

y = b/a

Asymptotes of a vertical hyperbola

y = a/b

Horizontal parabola

x = a(y-k)² + h

Vertical parabola

y = a(x-h)² + k

How to find a

a = 1/4c

Distance of vertex from focus and directrix

c

Vertical transverse axis

y²/a² - x²/b² = 1