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I am trying to plot the equations that describe the Cartesian locations of Bi-Cylinder coordinates. The equations are as follows:

x==(1.5 Sinh[n])/(Cosh[n]-Cos[p])   
y==(1.5 Sin[p])/(Cosh[n]-Cos[p])

I keep getting the following error

Options expected(instead of {p,0,2 pi}) in position 2 of Plot[{x,y},{n,-1,1},{p,0,2 pi},PlotRange All] an option must be a rule or a set of rules

I need help in understanding the error and how to rectify the situation and get the program to run correctly.

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    $\begingroup$ 1) Use Pi, not pi. Mathematica is case-sensitive. 2) What are you trying to plot exactly? $\endgroup$
    – MarcoB
    Jun 21, 2016 at 22:07
  • $\begingroup$ It's unclear what you want to visualize, but I like how ParametricPlot[{(1.5 Sinh[n])/(Cosh[n] - Cos[p]), (1.5 Sin[p])/(Cosh[n] - Cos[p])}, {n, -1, 1}, {p, 0, 2 Pi}] looks :) $\endgroup$
    – BlacKow
    Jun 21, 2016 at 22:11

2 Answers 2

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Using approach suggested by @Mikado except Table is moved inside of ParametricPlot

ParametricPlot[
 Evaluate@
  Table[
   Tooltip[{
     (1.5 Sinh[n])/(Cosh[n] - Cos[p]),
     (1.5 Sin[p])/(Cosh[n] - Cos[p])},
    n],
   {n, -1, 1, 2/7}],
 {p, 0, 2 Pi},
 PlotRange -> All,
 AspectRatio -> Automatic,
 PlotLegends -> Range[-1, 1, 2/7]]

enter image description here

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You need to use ParametricPlot. For example

Show[Table[ParametricPlot[{(1.5 Sinh[n])/(Cosh[n] - 
   Cos[p]), (1.5 Sin[p])/(Cosh[n] - Cos[p])}, {p, 0, 2 Pi}, 
   PlotRange -> All, AspectRatio -> Automatic], {n, -1, 1, 2/7}]]

gives

enter image description here

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