$ x^2 + y^2 = 4x+4$
How to put it in the standard form: $(x-a)^2 + (y-b)^2 = r^2$
$ x^2 + y^2 = 4x+4$
How to put it in the standard form: $(x-a)^2 + (y-b)^2 = r^2$
$(x-a)^2+(y-b)^2=r^2\implies x^2+y^2-2ax-2by+a^2+b^2-r^2=0$
Comparing with, $x^2+y^2-4x-4=0$
$b=0$ (coefficient of $y$)
$2a=4\implies a=2$ (coefficient of $x$)
$a^2+b^2-r^2=-4,2^2+0^2-r^2=-4,r^2=8$ (constant term)
So, $(x-2)^2+(y-0)^2=(2\sqrt 2)^2$
Or directly, $x^2+y^2-4x-4=(x)^2-2\cdot x\cdot 2+(2)^2+(y)^2-4-4$ $=(x-2)^2+(y)^2-(2\sqrt 2)^2$
So, $(x-2)^2+(y)^2-(2\sqrt 2)^2=0$ or $(x-2)^2+(y)^2=(2\sqrt 2)^2$