Learning Resources

Outcomes

In this lesson you will learn

• Use transformations to derive the equations of circles with centres off the origin.

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 write the equation of a circle with centre at the origin and given radius.
• Have an understanding of transformations and what effect certain transformations have on the equations of the figures involved.
• The use of mapping notation to describe transformations.