The graph of the equation Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 is either a conic or degenerate conic. Please g

The graph of the equation

Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

is either a conic or degenerate conic. Please give me an example or two for the "degenerate conic" case. What are the conditions for the graph to be a degenerate conic? What exactly does "a degenerate conic" mean?
Update: Can the graph of with equation Ax^2 + Cy^2 + Dx + Ey + F = 0 also be a conic, except for some degenerate cases (in which a points, one or two lines, or no graph is obtained)? Please also give me some examples for this (the book doesn't give any). I think this equation can be obtained by the rotation of... show more Can the graph of with equation

Ax^2 + Cy^2 + Dx + Ey + F = 0

also be a conic, except for some degenerate cases (in which a points, one or two lines, or no graph is obtained)? Please also give me some examples for this (the book doesn't give any). I think this equation can be obtained by the rotation of axes with some angle to eliminate Bxy -- that is, for B = 0.
5 answers 5