Equation of an Ellipse
Standard Form equation
How to Create an Ellipse Demonstration
An ellipse is the set of all points in a plane such that the sum of the distances from T to two fixed points F_{1} and F_{2} is a given constant, K.
TF_{1} + TF_{2} = K F_{1} and F_{2} are both foci(plural of focus) of the ellipse.
The major axis is the segment that contains both foci and has its endpoints on the ellipse. These endpoints are called the vertices. The midpoint of major axis is the center of the ellipse.
The minor axis is perpendicular to the major axis at the center, and the endpoints of the minor axis are called covertices.
The vertices are at the intersection of the major axis and the ellipse.
The covertices are at the intersection of the minor axis and the ellipse.
You can think of an ellipse as an oval.
Picture of an Ellipse
Standard Form Equation of an Ellipse
The general form for the standard form equation of an ellipse is
Horizontal Major Axis Example
Example of the graph and equation of an ellipse on the Cartesian plane:
 The major axis of this ellipse is horizontal and is the red segment from (2,0) to (2,0)
 The center of this ellipse is the origin since (0,0) is the midpoint of the major axis
 The value of a = 2 and b = 1
Vertical Major Axis Example
Example of the graph and equation of an ellipse on the Cartesian plane
 The major axis of this ellipse is vertical and is the red segment from (2,0) to (2,0)
 The center of this ellipse is the origin since (0,0) is the midpoint of the major axis
 The value of a = 2 and b = 1
Practice Problem
Graph of Ellipse from the Equation
The problems below provide practice creating the graph of an ellipse from the equation of the ellipse. All practice problems on this page have the ellipse centered at the origin.
Click here for practice problems involving an ellipse not centered at the origin. a = 5
 b = 2
 a = 5
 b = 3
 a = 6
 b = 5
 a = 6
 b = 5
 a = 6
 b = 2
 a = 6
 b = 1
 a = 6
 b = 2
 a = 7
 b = 3
 a = 3
 b = 2

Related:
 Equation of Ellipse
 Major Axis of Ellipse
 Minor Axis of Ellipse
 Vertices
 Covetices
 focus of an ellipse
 Is a circle an ellipse?
 Eccentricty of Ellipse
 area of an ellipse
 Orbits of Planets as ellipses
 Translate ellipse
 images
 Worksheet Version of this Web page (same questions on a worksheet)