> For question 2, it is possible to calculate the coefficients for the equation,
> but how do we plot the ellipse?
> 

There are several possible ways. The challenge beyond normal function
plotting is that the ellipse is specified as an equational constraint.
Two main approaches involve either find a parameterization of the ellips, 
or alternatively explicitly using this equational constraint and finding 
the curve that satisfies it.

1. Parameterize the curve. This can be done in several ways. One
apprach is to start with a circle (which is generated using sin and
cos functions) and suitably transform this using the ellips paramteres
into a plot of the ellipse.

2. Directly search for 0's to the equation. A naive approach would be
to guess and x and y interval containing the ellipse, then think of
the ellipse equation as a function of (x,y) and evaluate this function
on the interval. (You can view the result using "mesh"). The ellipse is 
the zero-curve to this 3D function, and you have to extract it by e.g. 
finding the points where it changes sign.

Note that in either method you can/should check that points given in
the exercise are on your curve.

Martin
-- 
Martin Jagersand                       E-mail: c340@ugrad.cs.ualberta.ca
Computing Science                      WWW:    www.cs.ualberta.ca/~jag
University of Alberta                  
Edmonton, Alberta, CANADA, T6G 2E8