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.

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 the 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 co-vertices.

The vertices are at the intersection of the major axis and the ellipse.

The co-vertices are at the intersection of the minor axis and the ellipse.

Standard Form Equation of an Ellipse

The general form for the standard form equation of an ellipse is shown below..

In the equation, the denominator under the $$ x^2 $$ term is the square of the x coordinate at the x -axis.

The denominator under the $$ y^2 $$ term is the square of the y coordinate at the y-axis.

Practice Problem

Problem 1

Can you determine the values of a and b for the equation of the ellipse pictured in the graph below?

Problem 2

Can you determine the values of a and b for the equation of the ellipse pictured below?

Problem 3

What are values of a and b for the standard form equation of the ellipse in the graph?

More Practice writing equation from the Graph

Problem 4

Examine the graph of the ellipse below to determine a and b for the standard form equation?

Problem 5

Examine the graph of the ellipse below to determine a and b for the standard form equation?

Problem 6

What is the standard form equation of the ellipse in the graph below?

Problem 7

What is the standard form equation of the ellipse in the graph below?

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.