Centre for Distance Learning and Innovation

Outcomes

In this lesson you will

Rewrite the general and standard forms of the equation of a circle in transformational form.
Use the transformational form to gain information about, and help with the graphing of, the circle.

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.

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

How to rewrite the equations of other functions in transformation form.
How to use various transformations like stretching and sliding to obtain the graph of a given equation from some standard position of the equation.