Get a ParametricPlot with interactive parameter, to trace the coordinates?

Questions
, , ,
1

I have noticed that by using the Free-form input for parametric plots, clicking the plus icon in the upper right-hand corner displays additional results provided by Wolfram|Alpha. One of which is a slider for the parameter which I am using to create the plot.

For example:

screenshot.png
screenshot.png562×105 6.99 KB

Clicking on the plus sign, I can see the plot, with a text balloon saying:

this subpod is selected. Press shift-enter to request this subpod form Wolfram|Alpha.

Doing what it says I get on a new line in my notebook the parametric plot with an option to trace the curve, somewhat like Manipulate does.

My question is: How can I create such a plot with Mathematica input, not using the free-form?
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=screenshot.png&userId=1344988

2

ParametricPlot[{Cos[t], Sin[2 t]}, {t, 0, 2 Pi}]

3

DynamicModule[{tr = 1},
Column[{
Show[
ParametricPlot[
{Cos[t], Sin[2 t ]}, {t, 0, 2 Pi},
GridLines →
Dynamic[List /@ CurrentValue[{“MousePosition”, “Graphics”}]]
, PlotStyle → Directive[Thin, Gray]
],
Graphics@{Dynamic[First@ParametricPlot[
{Cos[t], Sin[2 t ]}, {t, 0.0001, 2 Pi tr},
PlotStyle → Thick
] /. Line → Arrow]
}
, ImageSize → Large],
Slider@Dynamic@tr
}]
]

4

Thanks. That’s what I was looking for.

But, is there any way to extract out this command you wrote of the Wolfram|Alpha subpod?