Learning Resources

Outcomes

In this lesson you will learn

• Use coordinate geometry to examine the equation of a circle with center at 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.

Introduction

In this section, you will examine equations of circles, apply transformations to basic circular equations, and graph the results.

You will learn how to take a circular equation in general form and rewrite it in standard and then transformational form.

You will examine the transformations that change a circle into an ellipse.

This section should take you between 5.5 and 6.5 hours to complete.

Prerequisites

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

• Plot points and draw circles on a coordinate grid.
• The distance formula.
• The Pythagorean Theorem.