conics

(x-h)²+(y-k)²=r²

circle

(x-h)²/a² + (y-k)²/b² = 1

horizontal ellipse

(x-h)²/b² + (y-k)²/a² = 1

vertical ellipse

c² = a²-b²

ellipse c equation

(x-h)²/a² - (y-k)²/b² = 1

horizontal hyperbola

(y-k)²/a² - (x-h)²/b² = 1

vertical hyperbola

(x-h)² = 4p(y-k)

vertical parabola

y = (x-h)²/4p + k

other vertical parabola

c² = a² + b²

hyperbola c equation

(y-k)² = 4p(x-h)

horizontal parabola