- #1
Sven
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Homework Statement
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?
Homework Equations
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?