Ellipse

An ellipse is a plane curve whose points have a constant sum of distances from two fixed points called foci. A circle is the special case in which the foci coincide.

Focus (geometry): A fixed point used to define a conic section; an ellipse has two foci. The two fixed points in the ellipse’s constant-distance-sum definition.
Distance: A measure of the separation between two points in a geometric space. The ellipse is defined by adding distances from each point on the curve to its foci.
Kepler's laws of planetary motion: Three laws describing planetary orbits, including their elliptical shapes and changing orbital speeds. Kepler’s first law identifies planetary orbits as ellipses with the Sun at one focus.
Circle: A plane curve whose points are all the same distance from a fixed center. A circle is the limiting symmetric case of an ellipse, with coincident foci.
Eccentricity (mathematics): A number measuring how much a conic section departs from circular shape. For an ellipse, eccentricity measures how far its foci lie from the center relative to its size.
Perpendicular bisector: A line that meets a segment at its midpoint at a right angle. The perpendicular bisector of the foci segment is the ellipse’s major axis.
Ellipse drawing methods: Geometric procedures for constructing an ellipse, including the string-and-pins method. A taut string fixed at two pins traces points with a constant sum of focal distances.
Parabola: A conic section whose points are equally distant from a fixed focus and a directrix. Unlike an ellipse, a parabola is unbounded and has one focus.
Ellipse equation: An algebraic equation describing an ellipse, commonly written in coordinates centered on its axes. The standard equation translates the ellipse’s axis lengths into a coordinate description.
Major axis: The longest diameter of an ellipse, passing through its center and both foci. Its length sets the constant sum of focal distances and the ellipse’s longest span.

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