Conic Sections in Polar Coordinates
- Author:
- dthurston
- Topic:
- Conic Sections, Coordinates
What effect do e, p*, cosine, sine, + and - have on the type of conic section generated?
We have discussed in class that we can model a conic section with horizontal and vertical axes and a focus at the pole using the general equations:
or
What effect do each of these parameters have on a) the type of conic section we have; and b) what that conic section looks like?
In the applet below, please drag the bars for "e" and "p*" to look for their effects. Please investigate the effect of the trigonometric function used and the sign (+ or -) by looking at the different curves generated by these forms. (Be aware that you can only have one box checked at the same time).
Note: Your curve is in purple. Your focus (or one of them) is located at the pole. Your directrix is shown in green.
What effect does e have?
What effect does p have?
How do the curves defined using sine and cosine differ from each other?
How do the curves using "+" and "-" differ from each other?