Ellipses
Posted: April 26th, 2011, 5:34 pmAn ellipse is the set of all points (x, y) in a plane, the sum of whose distances from two distinct fixed points (foci) is constant.
Standard equation
Center (h, k)
If the denominator under x2 is LARGER, the major axis is horizontal.
If the denominator under the y2 is LARGER, the major axis is vertical.
The LARGER denominator is ALWAYS a2
The foci lie on the major axis, c units from the center, with
ECCENTRICITY
Eccentricity e is the ovalness of an ellipse.
0 < e < 1 for EVERY ellipse
The close the foci to the center, the more circular the ellipse.
Standard equation
Center (h, k)
| Major axis is horizontal Major axis is vertical |
If the denominator under x2 is LARGER, the major axis is horizontal.
If the denominator under the y2 is LARGER, the major axis is vertical.
The LARGER denominator is ALWAYS a2
The foci lie on the major axis, c units from the center, with
ECCENTRICITY
Eccentricity e is the ovalness of an ellipse.
0 < e < 1 for EVERY ellipse
The close the foci to the center, the more circular the ellipse.