What is the distance between the center of the circle with equation \(x^2+y^2=6x-8y+24 \) and the point (-3,-12)?
+128454 Rearrange the given equation as
x^2 - 6x + y^2 + 8y = 24 complete the square on x and y
x^2 - 6x + 9 + y^2 + 8y + 16 = 24 + 9 + 16
(x -3)^2 + (y + 4)^2 = 49
The center of the circle is ( 3, -4)
So.....the distance between the center and (-3, -12) is given by :
sqrt [ (-3 - 3)^2 + (-12 - - 4)^2 ] =
sqrt [ (-6)^2 + (-8)^2 ] =
sqrt [ 36 + 64 ] =
sqrt (100) =
10 units
