CIRCLE LESSON - INTRODUCTION

Equation of the Circle with Center at (0,0)

The generating equation for a circle with center at (0,0) is: $${𝐫}^{\mathrm{𝟐}}={𝐱}^{\mathrm{𝟐}}+{𝐲}^{\mathrm{𝟐}}$$

This means that the (x,y) coordinate pair associated with each point of the graph will always satisfy this equation, where r is the distance from the center to any point on the circle - called the radius. Notice how much this looks like the Pythagorean Theorem. Do you know why? Because it *IS* the Pythagorean Theorem! If we take the square root of both sides we get the distance formula (with center at the origin):

$$𝐫=\sqrt{{𝐱}^{\mathrm{𝟐}}+{𝐲}^{\mathrm{𝟐}}}$$

And what is the very definition of the locus of points of a circle? All points equiDISTANT from a given point - the center! Page 9 of the module goes into detail on this very important equation. Make to read it thouroughly before you do the interactive activity below.

Module

Activity

This activity is tied to Page 9 of the Module above. Go to Page 9 and then use the activity. There is a small Play Button on the bottom right of the activity. Hit the button and in your mathematics notebook record how the circle graph and formula change. Hint: You may want to put the activity in Fullscreen mode, by hitting the sqaure button on the bottom right of the activity window.

FORMULA SHEET #1

LESSON #2