Discriminant test for non degenerate conics?

Question

What is the discriminant test for non degenerate conics?

Answer 1

The above link appears to be a determinant test for conics, degenerate and non degenerate. Did you mean determinant test?
A degenerate conic would be one that graphs as a line, a pair of intersecting lines, or a point. Algebraically, there are no second degree terms, so the coefficient on the second degree terms would be 0.
All conics can be expressed as second degree polynomial equations, and the discriminant of a second degree polynomial equation is the familiar b^2-4ac from the quadratic formula. For parabolas, if the discriminat is 0, the function touches the x axis at exactly one point. If the discriminat is > 0 the function crosses the x axis twice, and if the discriminat is < 0 the function does not cross the x axis.
For other conics other than the degenerate points and lines, it is possible to complete the square on both variables rather than only on the x, and to consider the discriminant with respect to either variable, with the result of finding if the graph crosses the x or y axis once, twice, or not at all. This would be useful in determining if the curve is a hyperbola, ellipse, or circle, and how and where the graph is situated on the plane.
Caveat: I was not able to find an online reference to a discriminat test for non degenerate conics, I am simply generalising here from the discriminat test for parabolas. And if you meant determinant test, go with what northstar said.

Answer 2

Here is a link to the tests for different types of conic sections--degenerate and non-degenerate.

http://mathforum.org/dr.math/faq/formulas/faq.analygeom_2.html#twogenquads