Determine if the following polar conic equations are parabolas, circles, ellipses, or hyperbolas.

Using Derive:

- Prepare the program for graphics.
- If the first menu item is
*Algebra*then press . - Press for
*Author*. - Enter the function
r=3/(3-2cos ) - Press to get the plot window.
*Now we need to prepare Derive to graph in polar coordinates.* - Press to enter the options menu.
- Now press to enter the state menu.
- Finally, press and then
to tell Derive to graph using continuous polar coordinates.
**Note: Derive will continue to graph in polar coordinates for the remainder***of the session or until the state is chaged back to rectangular.*

- Now press and then to see the graph.

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r=2.5 - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.* - Now press and then
to see the new graph drawn.

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r=1/(1=cos ) - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.* - Now press
*Derive can have troubles with parabolas/hyperbolas when their input value is pi.**To compensate for this we will change the end values to -3 and 3.*- Change the
**-3.1416**to**-3**and then press- Then change the
**3.1416**to**3**and then press- The graph should now draw fine.
- Next press to return to the algebra window.
- Press for
*Author*.- Enter the function
r= 1/(1-1.2 cos - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.*- Now press
*Derive can have troubles with parabolas/hyperbolas when their input value is pi.**To compensate for this we will change the end values to -2.5 and 2.5.*- Change the
**-3**to**-2.5**and then press- Then change the
**3**to**2.5**and then press- The graph should now draw fine.
- We now have the following graphed.

To find out more about why we saw the shapes we did, see Eccentricity and Polar Conics

This document was originally written by Richard Rupp.