Answer
See below.
Work Step by Step
If we plug in the respective $x$ and $y$ values of $(x,y)$, we can check if it satisfies the equation, if it does, it is on the graph, if it doesn't it is not on the graph.
Hence here: $(0,2)\rightarrow0^2+2^2=0+4=4$, so it is on the graph
$(-2,2)\rightarrow(-2)^2+2^2=4+4=8\ne4$, so it is not on the graph
$(\sqrt2,\sqrt2)\rightarrow\sqrt2^2+\sqrt2^2=2+2=4$, so it is on the graph