# Plotting a set of parameters

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.

• 1) Use Pi, not pi. Mathematica is case-sensitive. 2) What are you trying to plot exactly? – MarcoB Jun 21 '16 at 22:07
• 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 :) – BlacKow Jun 21 '16 at 22:11

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]] 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 