Question

Determine what the graph of x^2+4xy+y^2-32=0 is.

a.) a hyperbola
b.) a line
c.) an ellipse
d.) a parabola

Answer 1

http://www.wolframalpha.com/input/?i=plot+x^2%2B4xy%2By^2-32%3D0

Answer 2

According to wolframalpha it is a hyperbola. Why?

Answer 3

Think
\[
B^2 - 4 AC
\]

Answer 4

\[
x^2+4xy+y^2-32=0 \\
A x^2 + B xy + Cy^2 -32=0\\
B^2- 4 A C = 4^2 - 4 (1)(1)= 16-4=12>0
\]
It is a hyperbola

Answer 5

Did you understand what I did