SOLUTION: Write the equation of the circle in general form if the center is (2,3) and the radius is 5. (General Form: Ax^2+By^2+Cx+Dy+E=0)

Question 383004: Write the equation of the circle in general form if the center is (2,3) and the radius is 5. (General Form: Ax^2+By^2+Cx+Dy+E=0)
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
Write the equation of the circle in general form if the center is (2,3) and the radius is 5. (General Form: Ax^2+By^2+Cx+Dy+E=0)

if center (0,0): x^2 + y^2 = r^2 or in general form x^2 + y^2 - r^2 = 0,
A = 1, B = 1, C = 0, D = 0, E = -r^2
if center (h,k): (x - h)^2 + (y - k)^2 = r^2
or multiplying with FOIL (First Outer Inner Last):
x^2 - 2hx + h^2 + y^2 - 2ky + k^2 = r^2
or in general form: x^2 + y^2 - 2hx - 2ky + h^2 + k^2 - r^2 = 0,
A = 1, B = 1, C = -2h, D = -2k, E = h^2 + k^2 - r^2
center: (2,3), radius: 5
A = 1, B = 1, C = -2h = -2 * 2 = -4, D = -2k = -2 * 3 = -6,
E = 2^2 + 3^2 - 5^2 = 4 + 9 - 25 = 13 - 25 = -12
general form: x^2 + y^2 - 4x - 6y - 12 = 0

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