Final answer:
To find the equation of a circle with a given diameter, we need to find the center and the radius. The center can be found by finding the midpoint of the diameter, and the radius can be found by calculating the distance between the center and one of the endpoints of the diameter. The equation of the circle is then given by (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
Step-by-step explanation:
To find the equation of a circle, we need to know the center and the radius. In this case, the line segment C(3, -4) to C(-3, 4) is the diameter, so we can find the center by finding the midpoint of the diameter. The midpoint formula is given by ((x1 + x2)/2, (y1 + y2)/2). So, the center is ((3 - 3)/2, (-4 + 4)/2) = (0, 0). Now, we can find the radius by finding the distance between the center and one of the endpoints of the diameter. The distance formula is given by sqrt((x2 - x1)^2 + (y2 - y1)^2). So, the radius is sqrt((3 - 0)^2 + (-4 - 0)^2) = sqrt(9 + 16) = sqrt(25) = 5.
Therefore, the equation of the circle is (x - 0)^2 + (y - 0)^2 = 5^2, which simplifies to x^2 + y^2 = 25.