Answer:
[tex]\huge\boxed{Center = (3,3),Radius = 2\sqrt{15} }[/tex]
Step-by-step explanation:
Given equation is
[tex]x^2 + y^2 -6x-6y -42 = 0[/tex]
Adding 42 to both sides
[tex]x^2 + y^2 -6x-6y = 42\\[/tex]
Completing squares
[tex]x^2 -6x+y^2 -6x = 42\\(x)^2 - 2(x)(3) +y^2 - 2(y)(3) = 42[/tex]
Adding (3)² => 9 and (3)² => 9 to both sides
[tex](x-3)^2+(y-3)^2 = 42+9+9\\(x-3)^2 + (y-3)^2 = 60\\(x-3)^2 (y-3)^2 = (2{\sqrt{15})^2}[/tex]
Comparing it with [tex](x-h)^2+(y-k)^2 = r^2[/tex] where Center = (h,k) and Radius = r
We get:
Center = (3,3)
Radius = [tex]2\sqrt{15}[/tex]
