Conic sections

An ellipse is the set of points whose sum of distances to two fixed foci is constant. Its standard graphing form is \(\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\) for a horizontal major axis, or \(\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1\) for a vertical major axis. The center \((h,k)\) is the midpoint of the vertices, \(a\) is half the distance between vertices, and \(c\) is half the distance between foci. The relationship \(c^2=a^2-b^2\) gives the missing denominator.