SOLUTION: How do you identify whether x^2+3y^2-2x+36y+100=0 is a circle, hyperbola, parabola, or an ellipse.

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Question 133096: How do you identify whether x^2+3y^2-2x+36y+100=0 is a circle, hyperbola, parabola, or an ellipse.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
How do you identify whether x%5E2%2B3y%5E2-2x%2B36y%2B100=0 is a circle, 
hyperbola, parabola, or an ellipse.


Rule:

For the equation:

Ax%5E2+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0

1. If A = C, the equation is of a circle
2. If A or C is 0 but not both 0 the equation is of a parabola.
3. If A and C have the same sign, but are not equal, the equation is of an ellipse.
4. If A and C have opposite signs, the equation is of a hyperbola.


Your equation is

x%5E2+%2B+3y%5E2+-+2x+%2B+36y+%2B+100=0

Comparing that to

Ax%5E2+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0

A=1, C=3 (It doesn't matter about D, E, and F)


A and C have the same sign but they are not equal, so the graph is of
an ellipse.

Edwin