Conic Sections
rename
Updated
2009-02-03 09:53
Conic Sections
In general, Conic Sections satisfy: Ax2+Bxy+Cy2+Dx+Ey=F.| Conic Section | Equation |
|---|---|
| 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 | Eccentricity e |
|---|---|
| Circle | e=0 |
| Parabola | e=1 |
| Ellipse | e=c/a, 0 |
| Hyperbola | e=c/a, e>1 |
