Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle.

$$x^2+y^2-2x-2y=14\\\\
(x^2-2x)+(y^2-2y)=14\\\\
\mbox{now you have to complete the 2 squares}\\\\
(x^2-2x+1)+(y^2-2y+1)=14+1+1\\\\
(x-1)^2+(y-1)^2=16\\\\
(x-1)^2+(y-1)^2=4^2\\\\$$

 

Centre (1,1) radius =4

(x-1)² + (y-1)² = 4²  Expand and rearrange to see that this is the same as your equation.

center = (1, 1) radius = 4