# Parametric plot

I want to plot x = u Cos[Phi] + v Cos[(u Phi)/v] and y = u Sin[Phi] - v Sin[(u Phi)/v]in a parametric graph for u = 3 and v = 5. This is my command:

ParametricPlot[{x, y} /. {u -> 3, v -> 5}, {Phi, 0, 2 Pi},
PlotRange -> All]


I think it was supposed to show two circles and it's not.

Also, for the same u and v values, if the angular velocity of the inner circle about its own center is 0.1 rad/sec, and the time taken for an arbitrary initial contact point to return to the same con figuration.

• Definitely not a circle. – march Apr 15 '16 at 5:31
• Hmm that's what I thought too. But then the problem asks what are the radii for the inner and outer circles so I'm not sure – Ccyan Apr 15 '16 at 5:40

p1 = ParametricPlot[{x, y} /. {u -> 3, v -> 5}, {Phi, 0, 10 \[Pi]},
PlotRange -> All]


v=2;

p2 = ParametricPlot[{v Cos[u], v Sin[u]}, {u, 0, 2 Pi},
PlotStyle -> Directive[Red, Opacity[1]]]


Show[p1, p2]


but do the Math by your self, because there are other circles

Edit - some sources and infos:

Natural Parametric Equations

Circle

How to | Plot Parametric Functions

How to | Create Plots

Have Fun!

• What do you mean other circles? And why did you use sin and cos to get the circle? I really don't get this – Ccyan Apr 15 '16 at 6:04