Are you sure you need to create a graph of
x^2 + y^2 = 0? It's not a very exciting graph...
If you really do need to do it for some reason, solve that equation for y and you get
y=√(-x^2), then put that into the y= function of the graphing calculator. I tried that with several different graphing calculators online and while a few rejected it because the square root of a negative number isn't a real number, most gave the correct answer of a single point at (0,0).
Of the calculators I found, I like
this one the best because it will let you overlay multiple different formulas on the same x-y axis (a useful feature at times).
edit: It doesn't appear to have advanced algebra functions like sine/cosine/tangent/etc, so you'll need a different tool if you need those, but it graphs the formula that you requested just fine...
edit again: If you go
here then click the "Free online graphing calculator" link, it has a version of the same tool that includes sin/cos/tan/abs/e/ln/log/deg/rad functions.