What is the distance between the center of the circle with equation \(x^2+y^2=6x-8y+24 \) and the point (-3,-12)?

Guest Oct 10, 2019

#1**+2 **

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

CPhill Oct 10, 2019