1. The problem statement, all variables and given/known data Suppose that A and C are not both 0. Show that the set of all (x,y) satisfying Ax^2 + Bx + Cy^2 + Dy + E = 0 is either a parabola, an ellipse, or an hyperbola (or a degenerate case: two lines, one line, a point, or 0.) Now consider separately the cases where A and B are both positive or negative, and where one is positive while theo ther is negative. When do we have a circle? 2. Relevant equations 3. The attempt at a solution Okay I don't know how to show this. Do I have to cut it up into 20-30 cases and prove for stuff like when A is not 0 and B is not 0 and everything else is 0, and when C is not 0 and D is not 0 and everything else is 0?