Learning Resources

Investigation 8: The Equation of an Ellipse

Test yourself

First rearrange the equation to put it in transformational form.
                 
The graph of the equation is an ellipse because the coefficients of the squares of the x and y variables are different. This means the stretch will be different in the two directions.

The centre of the ellipse is ( -1 , 2). The length of the minor axis is 6 and the length of the major axis is 8. The graph is below.
                          

2. First rearrange the equation to put it in transformational form.
                       

The graph of the equation is a circle because the coefficients of the squares of the x and y variables are the same. The centre of the circle is  ( 3 , -1) and the radius is 2. The graph is below.