Use Maple (pencil or pen and paper too!) to work these problems.

- 1.
- Consider the parametric curve:
- (a)
- What is the maximum domain for the parameter?
- (b)
- What is the period?
- (c)
- Plot the curve using either the ``plot'' command or the ``ParamPlot'' command.
- (d)
- Eliminate the parameter and show that the x-axis is an asymptote.
- (e)
- Write the curve in Cartesian form y=y(x) and plot it.

- 2.
- Consider the curve:
- (a)
- Plot the curve for t between 0 and Pi.
- (b)
- Plot the curve for t between 0 and 1,000. Why do you think the plots are different. Should there be a difference?
- (c)
- Determine the period.
- (d)
- Eliminate the parameter to obtain the Cartesian form y=y(x) and plot the curve.

- 3.
- The equation for the asteroid is:
- (a)
- Plot the graph of the asteroid.
- (b)
- Find the length of the part of the curve that is in the first quadrant.
- (c)
- Find the area bounded by the curve and the positive part of the x-axis and y-axis.

- 4.
- Describe the hypocycloid defined by:
Try out various values for a and r. Try a=28 and r=13 and decrease from there.