conics

circle equation

(x-h)² + (y-k)² =1

parabola right

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

parabola left

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

parabola up

(x-h)² = 4p(y-k)

parabola down

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

ellipse horizontal

(x-h)² /a² + (y-k)² /b² =1

vertical ellipse

(x-h)² /b² + (y-k)² /a² =1

horizontal hyperbola

(x-h)² /a² - (y-k)² /b² =1

vertical hyperbola

(y-k)² /a²- (x-h)² /b² =1

squared terms have the same coefficients

circle

only 1 squared term

parabola

squared terms with different coefficients but same signs

ellipse

squared terms have different signs

Hyperbola