Conic Sections

Conic Sections

In general, Conic Sections satisfy: Ax²+Bxy+Cy²+Dx+Ey=F.

Conic Section (memorize)	Equation (memorize)
Upward-opening parabola with vertex h,k	(x-h)2 = 4c(y-k), c>0
Downward-opening parabola with vertex h,k	(x-h)2 = 4c(y-k), c<0
Rightward-opening parabola with vertex h,k	(y-k)2 = 4c(x-h), c>0
Leftward-opening parabola with vertex h,k	(y-k)2 = 4c(x-h), c<0
Circle with center h,k	(x-h)2 + (y-k)2 = r2
Ellipse with x-interecepts h+-a and y-intercepts k+-b	(x-h)2/a2 + (y-k)2/b2 = 1
Hyperbola with x-intercepts h+-a	(x-h)2/a2 - (y-k)2/b2 = 1
Hyperbola with y-intercepts k+-b	(y-k)2/b2 - (x-h)2/a2 = 1
c=distance of foci from h,k, the center of an ellipse	c=sqrt(|a2-b2|)
c=distance of foci from h,k, the center of a hyperbola	c=sqrt(a2+b2)

 

Conic Section (memorize)	Eccentricity e (memorize)
Circle	e=0
Parabola	e=1
Ellipse	e=c/a, 0<e<1
Hyperbola	e=c/a, e>1