Pre-Calc Conics Formulas

parabola vertex

(h,k)

parabola focus

(h, k+p)

parabola directrix

y=k-p

parabola axis of symmetry

x=h

horizontal parabola focus

(h+p, k)

horizontal parabola directrix

x=h-p

horizontal parabola axis of symmetry

y=k

horizontal ellipse vertices

(h+-a, k) ellipse

horizontal ellipse co-vertices

(h, k+-b) ellipse

horizontal ellipse foci

(h+-c, k) ellipse

vertical ellipse vertices

(h, k+-a) ellipse

vertical ellipse co-vertices

(h+-b, k) ellipse

vertical ellipse foci

(h, k+-c) ellipse

to find c of ellipse

a^2-b^2=c^2

horizontal hyperbola vertices

(h+-a,k) hyperbola

horizontal hyperbola foci

(h+-c, k) hyperbola

horizontal hyperbola asymptotes

y=+- b/a (x-h)+k hyperbola

vertical hyperbola vertices

(h, k+-a) hyperbola

vertical hyperbola foci

(h, k+-c) hyperbola

vertical hyperbola asymptotes

y=+- a/b (x-h)+k hyperbola

to find c of hyperbola

a^2+b^2=c^2