What is the general form of the equation of the given circle with center a?
a: x2 + y2 + 6x − 24y − 25 = 0
b: x2 + y2 − 6x + 24y + 128 = 0
c: x2 + y2 + 6x – 24y + 128 = 0
d: x2 + y2 + 6x − 24y + 148 = 0

You'll want to work with the center-radius form of a circle equation for this. the center formula is (x – h)² + (y – k)² = r², where (h, k) is your center and r is your radius. plug in the information your circle gives you: A(-3, 12), radius = 5

(x + 3)² + (y - 12)² = (5)²  ... simplify the right side
(x + 3)² + (y - 12)² = 25 ... from here, you need to foil both of your binomials to convert this to the "general form" that your answer choices are in.
(x + 3)² = (x + 3)(x + 3) = x² + 6x + 9
(y - 12)² = (y - 12)(y - 12) = y² - 24y + 144

x² + 6x + 9 + y² - 24y + 144 = 25 ... combine like terms
x² + 6x + y² - 24y + 153 = 25 ... subtract 25
x² + 6x + y² - 24y + 128 = 0 is your equation. reorder it so that it's from the highest degree to the lowest: x² + y² + 6x - 24y + 128 = 0 is your result (C).