Sure, I'd be happy to help you solve this problem! Step 1: Read the problem and understand what it's asking for The problem is asking us to find the equation of a circle that passes through the three given points: (-1, 2), (3, 2), and (3, -2). Step 2: Identify what you need to find and choose the appropriate operation We need to find the equation of the circle in the form of (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Step 3: Plug in the numbers and variables and simplify the expression To find the equation of the circle, we first need to find the center of the circle. Since the circle passes through the two points (3, 2) and (3, -2), the x-coordinate of the center must be 3. The y-coordinate of the center is the average of the y-coordinates of these two points, which is (2 + (-2)) / 2 = 0. So the center of the circle is (3, 0). Next, we need to find the radius of the circle. We can use the distance formula to find the distance between the center and one of the points, such as (-1, 2). The distance is given by the formula √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) is the center of the circle and (x2, y2) is the point. Plugging in the values, we get: √((-1 - 3)^2 + (2 - 0)^2) = √(16 + 4) = √20 Finally, we can use the center and radius to write the equation of the circle: (x - 3)^2 + (y - 0)^2 = (√20)^2 Simplifying the expression, we get: (x - 3)^2 + y^2 = 20 Step 4: Check the answer to make sure it makes sense We can check the answer by plugging in one of the points from the problem, such as (3, 2), and making sure it satisfies the equation of the circle: (3 - 3)^2 + (2 - 0)^2 = 0 + 4 = 4 And (√20)^2 = 20, so the point satisfies the equation of the circle. Step 5: Write the answer clearly and concisely The equation of the circle that passes through the points (-1, 2), (3, 2), and (3, -2) is: (x - 3)^2 + y^2 = 20 This is our final answer.