Answer:
C) [tex]x^{2} + y^{2} - 12x + 2y + 21 = 0[/tex]
Equation of a circle:
[tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex]
Substitute into the equation
a = 6
b = -1
r = 4
[tex](x-6)^{2} +(y--1)^{2} =4^{2}[/tex]
[tex](x-6)^{2} +(y+1)^{2} =16[/tex]
Expand and Simplify
[tex](x-6)^{2} = x^{2} - 12x + 36[/tex]
[tex](y+1)^{2} = y^{2} + 2y + 1[/tex]
[tex]x^{2} - 12x + 36 + y^{2} + 2y + 1 = 16[/tex]
[tex]x^{2} + y^{2} - 12x + 2y + 36 + 1 = 16[/tex]
[tex]x^{2} + y^{2} - 12x + 2y + 36 + 1 - 16 = 0[/tex]
[tex]x^{2} + y^{2} - 12x + 2y + 21 = 0[/tex]
