2
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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.

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  • $\begingroup$ 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 $\endgroup$ – Gummala Navneeth Nov 24 '19 at 6:44
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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}}],
 {radius, 1/2, 3/2}]
| improve this answer | |
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  • $\begingroup$ Thanks alot. with Clear[t] . It worked. Is there a way , do the same without using {x = Cos[t], y = Sin[t]}. I wanted to use Circle[r] function and later use in manipulate to see what happens with varying r. $\endgroup$ – Gummala Navneeth Nov 24 '19 at 7:12
  • $\begingroup$ I'm able to use Manipulate function for radius of circle by introducing r in {x =r Cos[t], y =r Sin[t]} as well. I was curious to use Circle[] function. to specify x and y are on the circle. $\endgroup$ – Gummala Navneeth Nov 24 '19 at 7:29

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