I have a question on this math porblem involving identifying the graph of the equation....a simple question?

Question

What is the graph of this equation?

x^2+13xy+19y^2+5x-2y+13=0

The answer is a HYPERBOLA, but why???????
Is it because it has an xy???

I thought it was an ellipse because the AC>0

Answer 1

The formula

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

is a hyperbola if 4AC < B^2. If 4AC > B^2, then it's an ellipse.

4*1*19 = 76
13^2 = 169

So, hyperbola.

Answer 2

x^2 and y^2 will often produce a hyperbola, since a negative (-2) or a positive (2) squared will produce the same number (both are 4).

Answer 3

http://en.wikipedia.org/wiki/Hyperbola