Ellipse

Ellipses are described in several ways, each way having its own advantages and limitations:

1. The set of points, the sum of whose distances from two fixed points (the foci, which lie on the major axis) is constant. That is, P: PF₁ + PF₂ = constant.
2. The set of points whose distances from a fixed point (the focus) and fixed line (the directrix) are in a constant ratio less than 1. That is, P: PF/PD = e, where 0 < e < 1. The constant, e, is the eccentricity of the ellipse.
3. The set of points (x,y) in a Cartesian plane satisfying an equation of the form x²/25 + y²/16 = 1. The equation of an ellipse can have other forms, but this one, with the center at the origin and the major axis coinciding with one of the coordinate axes, is the simplest.
4. The set of points (x,y) in a Cartesian plane satisfying the parametric equations x = a cos t and y = b sin t, where a and b are constants and t is a variable. Other Earth travels around the Sun in a slighlty elliptical orbit. Illustration by Argosy. The Gale Group. parametric equations are possible, but these are the simplest.