Equations of Circles12-5

Equation of a Circle

What is the standard equation of the circle with a center at (5, -2) and a radius of 7?

What is the standard equation of each circle?

1. Center: (3, 5) Radius: 6

2. Center (-2, -1) Radius

3. What is the standard equation of each circle?

What is the standard equation of the circle with center (1, -3) that passes through the point (2,2)?

Step1: Distance formula to find the radius.

Step 2: Use the radius and center to write the equation + = + = 26

√ (𝑥2−𝑥1 )2+( 𝑦2−𝑦 1)2

√ (2−1 )2+(2−(−3))2

√ (1 )2+(5 )2

√1+25√26

4. What is the standard equation of the circle with center (4,3) that passes through the point (-1, 1)?

When you make a call on a cell phone, a tower receives and transmits the call. A way to monitor the range of a cell tower system is to use the equations of circles. Suppose the equation represents the position and the transmission range of a cell tower. What is the graph that shows the position and range?

Position is the center: (7, -2)Range is the radius: = 8

5. What is the center and radius of the circle with the equation . Graph the circle.

Answers for Questions 1-5

1. + = 2. + = 2 3. + = 4 4. + = 5.