This activity can be realized with TouchPlotLite (as well of course as TouchPlot)
It is well known the curve with polar equation
is a conic with focal point the origin, parameter p, excentricity e and focal axis the line with ϕ angle to the horizontal axis.
It is even better to see it, adjusting the three parameters p,e and ϕ...
Of course, parameters will have to be renamed a,b,c for use with TouchPlot.
- It is better to start with default values, so it might be good to reset (bottom option on the main menu) touchplot to default.
- Go to Polar curve menu, and enter the formula :
It will be easier in 3.2 version of touchplot, but for now, you need to use direct polish notation.
So the usual way to enter this formula would be : ÷, Vars, a, +, 2nd, 1, ×, b, cos, −, ϑ, Vars, c
(Not that long, nor difficult once you get the gripe on it...)
- Validate with OK, and leave the defaults (minimum angle, maximum, number of steps) as they are, from -π to π with 200 steps.
- Go back to Main menu, and now go to the Constants sub-menu. Define minimum value for a parameter to be 0, and leave the maximum at 5
Define minimum value for b to be 0 (for 0, you get a circle...) and leave the maximum at 5
You can leave defaults minimum and maximum values for c or change them to -3.14 and 3.14 if you prefer.
Activate the sliders for a,b and c parameters.
- Go back to main menu and go to the settings menu : activate Lock aspect ration option, so that you'll keep orthonormal scales.
- Graph it, and move the sliders, observe...