# How to plot a 2-D function of points which is a function of points from the Unit Circle

Consider the set of points $(x,y)$ such that $x^2+y^2=1$. Consider the functions $f(x,y)$ and $g(x,y)$ and I want to plot the set of 2-D points whose co-ordinates are $\left(f(x,y),g(x,y)\right)$. An example would be $f(x,y)=2x^2-xy+3y^2$ and $g(x,y)=xy$

f[x_, y_] := 2 x^2 - x y + 3 y^2
g[x_, y_] := x y

ParametricPlot[{f[Cos[t], Sin[t]], g[Cos[t], Sin[t]]}, {t, 0, 2 \[Pi]},
AxesOrigin -> {0, 0}]


ParametricPlot[{f[r Cos[t], r Sin[t]], g[r Cos[t], r Sin[t]]},
{t, 0, 2 \[Pi]}, {r, 0.8, 1.2}, AxesOrigin -> {0, 0}]


• The first curve is what I am also getting. But it shouldn't be correct. It should be a closed,continuous, convex set for the examples i have given. – dineshdileep Sep 24 '14 at 8:38
• @dineshdileep : I don't know what you mean. Can you visualize or figuring something of expecting plotting shape. – Junho Lee Sep 24 '14 at 11:54
• @dineshdileep: The first plot is closed, continuous, and convex. – DumpsterDoofus Sep 24 '14 at 16:19