Given an expression
color(white)("XXX")f(x,y)
and told that f(x,y)=color(red)(c) for some constant color(red)(c)
then (a,b) is a point on the graph of f(x,y) if and only if f(a,b)=color(red)(c)
For the given example:
color(white)("XXX")f(x,y)=x^2+4y^2
and we are told f(x,y)=x^2+4y^2=color(red)(4)
First point: color(black)(""(0,1))
Substituting (0,1) for (x,y) gives
color(white)("XXX")f(0,1)=0^2+4*(1^2)=color(red)(4)
So (0,1) is on the graph.
Second point: color(black)(""(2,0))
Substituting (2,0) for (x,y) gives
color(white)("XXX")f(2,0)=2^2+4*(0^2)=color(red)(4)
So (2,0) is on the graph.
Third point: color(black)(""(2,1/2))
Substituting (2,1/2) for (x,y) gives
color(white)("XXX")f(2,1/2)=2^2+4*((1/2)^2)=color(green)(5) !=color(red)(4)
So (2,1/2) is not on the graph.
