Circles: Equations of a Circle

Warm-Up Icon Section Warm-Up

Before we begin this section, let's review what we have already learned about circles and let's practice some skills we will need to have. We will build on this knowledge in this section.

think icon Think & Click: Section Warm-Up

Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

What is the definition of a circle?
 

A circle is all the points that are the same distance from a center point.
 

What is the radius and how is it related to the diameter?
 

The radius is the distance from the center to any point on the circle. The radius is one-half the diameter.
 

Use the Pythagorean Theorem to find the length of the hypotenuse of the following triangle.

Right triangle with legs 5 and 12 and hypotenuse h.
Right Triangle

 

52 + 122 = h2
25 + 144 = h2
169 = h2
13 = h
 

What is the distance from the point (2, 5) to the point (-7, -7)?
 

d equals the square root of the sum of the quantity negative 7 minus 2, the quantity squared, and the quantity negative 7 minus 5, the quantity squared; d equals the square root of sum of negative 9 squared and negative 12 squared; d equals the square root of 81 and 144; d equals the square root of 225; d equals 15
 

What are the coordinates of the following points?

Point A is 2 units to the left and 1 unit up; Point B is 2 units to the right and 4 units up; Point C is 3 units down
Points A, B and C

 

A (-2, 1)
B (2, 4)
C (0, -3)