Reb,
If all you have is a graph then you need to be able to tell enough from the graph to write an equation. You mentioned a circle, so if you have the graph of a circle and you can tell that the centre is at (2, 3) and the radius is 5 then you know that the equation is
(x  2)^{2} + (y + 3)^{2} = 5^{2}
Now expand and collect terms
(x  2)^{2} + (y + 3)^{2} = 5^{2}
x^{2}  4 x + 4 + y^{2} + 6 y + 9 = 25
x^{2}  4 x + y^{2} + 6 y  12 = 0
The difficult step of course is looking at the graph and being able to determine the centre and the radius.
Penny
