Final answer:
To find the equation of a circle given its center and a point on the circle, you can use the distance formula.
Step-by-step explanation:
To find the equation of a circle given its center and a point on the circle, you can use the distance formula. The equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2. In this case, the center of the circle is (3, -1) and a point on the circle is (4, 2). The radius can be found by calculating the distance between the center and the point on the circle using the distance formula: sqrt((x2 - x1)^2 + (y2 - y1)^2). Therefore, the equation of the circle is (x - 3)^2 + (y + 1)^2 = sqrt((4 - 3)^2 + (2 + 1)^2)^2.