Conics review

Equation of a circle

(x-h)²+(y-k)²=r²

Foci of a circle

None

Equation of a Vertical Parabola

(x-h)²=4p(y-k)

Equation of a horizontal parabola

(y-k)²=4p(x-h)

Focus of a horizontal parabola

h+p, k

Focus of a vertical parabola

h,k+p

Directrix of horizontal parabola

x=h-p

Directrix of vertical parabola

y=k-p

Equation of an ellipse (horizontal major axis)

(x-h)²/a²+(y-k)²/b²=1

Equation of an ellipse (vertical major axis)

(y-k)²/a²+(x-h)²/b²

how to find C of an ellipse

c²=a²-b²

Foci of a horizontal ellipse

h±c, k

foci of a vertical ellipse

h,k±c

Equation of a horizontal hyperbola

(x-h)²/a²-(y-k)²/b²

equation of a vertical hyperbola

(y-k)²/a²-(x-h)²/b²

How to find c of a hyperbola

c=a²+b²