The given equation of the circle is x² + y² - 30x + 100y + 2,500 = 0. To find the center and radius of this circle, we need to rewrite the equation in the standard form of a circle equation: (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
1. Complete the square for the x and y terms:
x² - 30x + y² + 100y = -2,500
(x² - 30x + 225) + (y² + 100y + 2,500) = -2,500 + 225 + 2,500
(x - 15)² + (y + 50)² = 225
2. Now, compare the equation with the standard form:
Center (h, k) = (15, -50) since h = 15 and k = -50.
Radius = √225 = 15 units.
Therefore, the center of the circle is at (15, -50) and the radius is 15 units.
