Lesson 2

Circles

In this lesson students will become familiar with the equations of circles and what the notation represents.

Definition: A circle is defined as the locus of all points that are equidistant from a given point called the center. The fixed distance from this point called the center is the radius. The chord that goes through the center of the circle is the diameter and is twice the radius.

The general form of the equation of a circle is , where represents the center of the circle and r represents the radius of the circle. If the location of the point to be considered is outside the circle, then the value in the equation will be greater than, if it is less than , it will be inside the circle. Click here to practice applying these relationships and definitions.

Practice Problem 1: A seismologist is trying to locate the epicenter of an earthquake. She has seismograph readings from the towns Alpha, Bravo, and Charlie listed in the table below.

Town	Distance to Epicenter
Alpha	17 miles
Bravo	10 miles
Charlie	5 miles

A. For each seismograph reading, graph the locus of all possible locations for the epicenter on the GSP graph.

B. Find the location of the epicenter and display your answer as an ordered pair, (x, y).

Practice Problem 2: A radio tower is located 25 miles east and 30 miles south of Hyte’s house. The radio signal is strong enough to reach homes within a 50 mile radius. Write an equation that represents all ground locations 50 miles from the radio tower. Can someone living 10 miles east and 5 miles north of Hyte receive the radio signal?