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Conic Sections

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Updated 2009-02-03 09:53

Conic Sections

In general, Conic Sections satisfy: Ax2+Bxy+Cy2+Dx+Ey=F.
Conic SectionEquation
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 ellipsec=sqrt(|a2-b2|)
c=distance of foci from h,k, the center of a hyperbolac=sqrt(a2+b2)
memorize

 

Conic SectionEccentricity e
Circlee=0
Parabolae=1
Ellipsee=c/a, 0
Hyperbolae=c/a, e>1
memorize

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