2. For the circle with equation (x – 2)2 + (y + 3)2 = 9, answer each question:

a) What are the coordinates of the center? none
b) What are the radius and diameter of the circle? 360
c) Graph the circle.

a. (h,k) = (2,-3)

b. r = sqrt 9 = 3
D = 2*r = 2 * 3 = 6

To answer question a) and find the coordinates of the center of the circle with the equation (x – 2)2 + (y + 3)2 = 9, we can use the standard form of a circle equation, which is (x - h)2 + (y - k)2 = r2. By comparing the given equation with the standard form, we can identify that the center of the circle is at the point (h, k) = (2, -3). Therefore, the coordinates of the center are (2, -3).

For question b), we can determine the radius and diameter of the circle from the equation (x – 2)2 + (y + 3)2 = 9. In the standard form of a circle equation, r2 represents the squared radius. Thus, in this equation, r2 = 9, which means the radius (r) is equal to the square root of 9, which is 3. The diameter of the circle is twice the radius, so the diameter is 2 * 3 = 6.

Question c) asks for graphing the circle. To graph the circle with the equation (x – 2)2 + (y + 3)2 = 9, we can use the coordinates of the center and the radius. Plot the center point (2, -3) on a graph, which marks the center of the circle. Then, draw a circle with a radius of 3 units around the center point. Ensure that the circle encompasses points that are 3 units away from the center in all directions.