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 boxes “Equation of the Circle,” “Show x -intercepts,” and “Show y -intercepts.” Change the value of r to 3 and the value of h to 4. Set the value of k to 0. What is the center of the circle? What is the equation of the circle? Are there any y -intercepts? If so, name them. Are there any x -intercepts? If so, name them.

(b) Leave the value of r set to 3 and the value of h set to 4. Change the value of k to −3. What is the center of the circle? What is the equation of the circle? Are there any y-intercepts? If so, name them. Are there any x-intercepts? If so, name them.

(c) Leave the value of r set to 3 and the value of h set to 4. Change the value of k to −4. What is the equation of the circle? Are there any y-intercepts? If so, name them. Are there any x-intercepts? If so, name them.

(d) Without graphing, how many x-intercepts will the graph of (x − 5)² + (y − 3)² = 9 have?

(e) Without graphing, how many y-intercepts will the graph of (x − 5)² + (y − 3)² = 9 have?