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## Ellipses

Math topics

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### Ellipses

An 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)

 $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$$\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$ Major axis is horizontalMajor 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 $c^2=a^2-b^2$

ECCENTRICITY

Eccentricity e is the ovalness of an ellipse. $e=\frac{c}{a}$

0 < e < 1 for EVERY ellipse

The close the foci to the center, the more circular the ellipse.
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