Posted by **dcw** on Thursday, March 25, 2010 at 11:21am.

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

- pre-calculus -
**Reiny**, Thursday, March 25, 2010 at 11:34am
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

- pre-calculus -
**trey**, Friday, March 26, 2010 at 10:26am
Find the transformed equation of the hyperbola xy = 4 when rotated 45?

- pre-calculus -
**dcw**, Friday, March 26, 2010 at 11:09am
Thanks reiny. This helped a lot.

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