Learning Resources

Outcomes

In this lesson you will

• Explore what transformations are necessary to change the equation of circle into the equation of an ellipse.
• Use the transformational form of the equation to sketch the graph of an ellipse.
• Be introduced to terminology associated with an ellipse, e.g. major and minor axes.

By the end of this section you should be able to:

• Analyze and translate between symbolic, graphic, and written representations of circles and ellipses.
• Translate between different forms of equations of circles and ellipses.
• Write proofs using various axiomatic systems and assess the validity of deductive arguments.
• Write the equations of circles and ellipses in transformational form and as mapping rules to visualize and sketch graphs.
• Demonstrate an understanding of the transformational relationship between a circle and an ellipse.
• Apply properties of circles.
• Solve problems involving the equations and characteristics of circles and ellipses.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• How to rewrite equations in transformational form.
• How to use the transformational form to sketch graphs.