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.
