I have $U(x,y)=xy$, $p_1=4$ and $p_2=1$. Income is unknown. Where do I start?
The way I would attack this is to solve the utility function $u(x,y)=xy$ subject to the budget constraint: $4x+y=m$. This is using Lagrange method It turns out that $x=m/8$ and $y=m/2$.
The Engel curve show the relationship between income and the quantity of the good demanded, so substitute values for $m$ and find the corresponding $x$ or $y$ demanded and plot the Engel curve for good x or good y.