I am slightly (a lot) confused between hypograph and epigraph and how the answers vary when the function is in R2 as compared to R3 .

So, for example, what would be the hypograph for f (x, y) = x^2 + y^2. The level curves of this function are like

Now is the red portion hypograph or the epigraph? According to me the red portion should be the hypograph and the white portion should be epigraph.? Am i correct?

Also, hypograph is the same as lower level set and epigraph is the same as upper level set?