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.

## Answer this Question

## Related Questions

- algebra 2 - Determine values for A, B, and C such that the equation below ...
- algebra 2 - Determine values for A, B, and C such that the equation below ...
- Algebra II - I am lost on this one!!! Determine values for A, B, and C such that...
- math - Classify the conic section as a circle, an ellipse, a hyperbola, or a ...
- algebra help please - I notice that other problems are answered in a timely ...
- Math - Classify the conic section 4x^2+5y^2-16x-30y+41=0 as a circle, ellipse, ...
- math - what are the general equations for the conic sections 1)parabola 2)circle...
- pre cal - What is the center of the conic whose equation is x^2 + 2y^2 - 6x + ...
- Pre Cal. - 1. Identify the conic section represented by: 9y^2+4x^2 - 108y+24x= -...
- geometry - I need images of Conic Sections: circle, ellipse, hyperbola and ...