# How to specify in Parametric Plot that variables are on circle?

I have 2 functions

a=2;
zx[x_, y_] := x + (a^2*x)/(x^2 + y^2);
zy[x_, y_] := y - (a^2*y)/(x^2 + y^2);


I want to draw a parametric plot of (zx,zy). Where x and y are on the circle of radius 1. So I tried this way

ParametricPlot[{zx[x, y], zy[x, y]},
Element[{x, y}, Circle[{0, 0}, 1]]]


and

ParametricPlot[{zx[x, y], zy[x, y]},
{Element[x, Circle[{0, 0}, 1]]},
{Element[y, Circle[{0, 0}, 1]]}]


Both are not working.kindly help me to plot the graph.

• I'm using Mathematica version 12 . I tried this With[{x = Cos[t], y = Sin[t]}, ParametricPlot[{zx[x, y], zy[x, y]}, {t, 0, 2*Pi}]] , it is not working Nov 24 '19 at 6:44

This works for me

Clear[a, zx, zy]

a = 2;
zx[x_, y_] := x + (a^2*x)/(x^2 + y^2);
zy[x_, y_] := y - (a^2*y)/(x^2 + y^2);

ParametricPlot[{x, y} = {Cos[t], Sin[t]};
{zx[x, y], zy[x, y]},
{t, 0, 2 π}]


Or this

Clear[t]
With[{x = Cos[t], y = Sin[t]},
ParametricPlot[{zx[x, y], zy[x, y]}, {t, 0, 2 π}]
]


Here is a method that uses Manipulate to change the radius of a Circle, but it is much too slow.

Manipulate[Show[Region[

ParametricRegion[{{zx[x, y], zy[x, y]},
{x, y} ∈ Circle[{0, 0}, radius]},
{{x, -10, 10}, {y, -10, 10}}]

], Frame -> True,
GridLines -> Automatic,
PlotRange -> {{-10, 10}, {-8, 8}}],