Standard Form equation
Before looking at the ellispe equation below, you should know a few terms.
More Examples of Axes, Vertices, Co-vertices
Example of the graph and equation of an ellipse on the
Example of the graph and equation of an ellipse on the :
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.
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.
More Practice writing equation from the Graph
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.$ \frac {x^2}{\red 2^2} + \frac{y^2}{\red 5^2} = 1 $
$ \frac {x^2}{25} + \frac{y^2}{9} = 1 \\ \frac {x^2}{\red 5^2} + \frac{y^2}{\red 3^2} = 1 \\ $
$ \frac {x^2}{25} + \frac{y^2}{36} = 1 \\ \frac {x^2}{\red 5^2} + \frac{y^2}{\red 6^2} = 1 \\ $
$ \frac {x^2}{36} + \frac{y^2}{25} = 1 \\ \frac {x^2}{\red 6^2} + \frac{y^2}{\red 5^2} = 1 \\ $
$ \frac {x^2}{36} + \frac{y^2}{4} = 1 \\ \frac {x^2}{\red 6^2} + \frac{y^2}{\red 2^2} = 1 \\ $
$ \frac {x^2}{1} + \frac{y^2}{36} = 1 \\ \frac {x^2}{\red 1^2} + \frac{y^2}{\red 6^2} = 1 \\ $
$ \frac {x^2}{36} + \frac{y^2}{4} = 1 \\ \frac {x^2}{\red 6^2} + \frac{y^2}{\red 2^2} = 1 \\ $
$ \frac {x^2}{36} + \frac{y^2}{9} = 1 \\ \frac {x^2}{\red 6^2} + \frac{y^2}{\red 3^2} = 1 $
Here is a picture of the ellipse's graph.
