Question

Explain how you got the answer

Answer 1

Answer:

$\huge\boxed{Center = (3,3),Radius = 2\sqrt{15} }$

Step-by-step 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

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

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

We get:

Center = (3,3)

Radius = $2\sqrt{15}$