precalculus
posted by dcw on .
How do i know if a conic section is a circle, ellipse, hyperbola, or parabola? based on it's equation such as 4x^2  y^2 + 24x + 4y + 28 = 0

General equation:
ax^2 + by^2 + cx + dy + e = 0
1) if a = b > circle
2) if both a and b are positive, but different, > ellipse
3) if a is positive and b is negative, > hyperbola
4) if either a or b, but not both, are zero > parabola
5) if both a and b are zero > straight line
so yours is a hyperbola 
Find the transformed equation of the hyperbola xy = 4 when rotated 45?

Thanks reiny. This helped a lot.