Equation of an Ellipse
Ellipses Centered at (0, 0)
Horizontal Major Axis
F'(-c, 0) F(c, 0)
Vertical Major Axis
F'(0, -c) F(0, c)
Ellipses Centered at (x0, y0)
Horizontal Major Axis
By removing the denominators, an equation of the following form is obtained:
A and B have the same sign.
F'(x0−c, y0) F(x0+c, y0)
Vertical Major Axis
F'(x0, y0−c) F(x0, y+c)
Examples
Find the elements and the equation of the ellipse with foci: F' = (−3, 0), F = (3, 0) and a major axis of 10.
Given the equation of the ellipse 
, determine the eccentricity and find the coordinates of the vertices and foci.
Find the equation of the ellipse that has a focus of F = (7, 2), vertex of A = (9, 2) and a center of C = (4, 2).
Given the ellipse equation 
, determine the center, semiaxes, vertices and foci.
Determine and plot the coordinates of the foci, vertices and eccentricity of the following ellipses:
1 
2 
3 
4 
