Question

Explain how you got the answer

Answer 1

`\huge\boxed{Center = (3,3),Radius = 2√(15) }`

Explanation:

Given equation is

`x^2 + y^2 -6x-6y -42 = 0`

Adding 42 to both sides

`x^2 + y^2 -6x-6y = 42\\`

Completing squares

`x^2 -6x+y^2 -6x = 42\\(x)^2 - 2(x)(3) +y^2 - 2(y)(3) = 42`

Adding (3)² => 9 and (3)² => 9 to both sides

`(x-3)^2+(y-3)^2 = 42+9+9\\(x-3)^2 + (y-3)^2 = 60\\(x-3)^2 (y-3)^2 = (2{√(15))^2}`

Comparing it with
`(x-h)^2+(y-k)^2 = r^2` where Center = (h,k) and Radius = r

We get:

Center = (3,3)

Radius =
`2√(15)`