Please help with graphing in geometry
posted by Knights on .
Find the largest real number x for which there exists a real number y such that x^2+y^2 = 2x+2y .
I think it is a circle, but how am i supposed to figure this out??

The standard equation for a circle is ...
(xa)^2 + (yb)^2=r^2
Lets play with your equation.
x^2+y^22x2y=0
x^22x + 1 + y^22y+1= 2 That wont work. We do have perfect squares on the left, but there is needed a zero on the right. Hmmm It is not a circle.
Lets look at if y is y<=0
if y is zero, then
x^2=2x or x can be any real number up to infinity, and there can be no larger x. So the answer is x=inf is the largest real number. Yes, y=0 is a real number.