Exercise 2.  Sketch the curve    

2 (a).  for  .  

Hint: Use  ,  and     and eliminate the parameter  t.

Solution 2 (a).

See text and/or instructor's solution manual.

    Use  ,  and substitute      and get which can be written in the form
,  which is a parabola oriented sideways with vertex at and opening to the right.

    For ,  the curve    is the portion of the parabola    from  .

We are done.   

Aside.  We can let Mathematica double check our work.

        The curve    for  ,   and  

        the initial point is    and the terminal point is  .  

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell