Open the “Circle” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.

(a) Check the box “Equation of the Circle” and uncheck the boxes “Show x -intercepts” and “Show y -intercepts.” Use the sliders to set the values of h and k to 0, and the value of r to 1. What is the center of the circle? What is the radius of the circle? What is the equation of the circle?

(b) Use the slider to change the value of r from 1 to 3. What is the equation of the circle whose center is the origin and radius is 3?

(c) Use the slider to change the value of r from 3 to 5. What is the equation of the circle whose center is the origin and radius is 5?

(d) Set the value of r to 3. Change the value of h to 2 and the value of k to 1. What is the center of the circle? What is the equation of the circle?

(e) Leave the value of r set to 3 and the value of k set to 1. Change the value of h to − 2. What is the center of the circle? What is the equation of the circle?

(f) L eave the value of r set to 3 and the value of h set to −2. Change the value of k to − 2. What is the equation of the circle?

(g) Suppose the equation of a circle is (x − 5)² + ( y + 7)² = 36. What is the center and radius of the circle?