SOLUTION: How do you know the difference between a circle or an ellipse? for an example.. 7x^2 + 7y^2 - 10x + 14y - 20 = 0 is this a circle or an ellipse? i know its not a parabo

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Question 447854: How do you know the difference between a circle or an ellipse?
for an example..
7x^2 + 7y^2 - 10x + 14y - 20 = 0
is this a circle or an ellipse?
i know its not a parabola, neither A nor C is zero, and A and C have the same sign, which its not an hyperbola.
Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do you know the difference between a circle or an ellipse?
for an example..
7x^2 + 7y^2 - 10x + 14y - 20 = 0
is this a circle or an ellipse?
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If the x^2 and the y^2 have equal coefficients,
the graph is a circle.
If they have different signs the graph is a hyperbola.
If they have the same sign but different values the
graph is an ellipse.
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Cheers,
Stan H.
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i know its not a parabola, neither A nor C is zero, and A and C have the same sign, which its not an hyperbola.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Ax%5E2+%2B+Bxy+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0
The conic sections described by this equation can be classified with the discriminant B%5E2++-+4AC.
If the conic is non-degenerate, then:
--> if B%5E2++-+4AC < 0, the equation represents an ellipse;
**if A = C and B = 0, the equation represents a circle, which is a special case of an ellipse;
--> if B%5E2++-+4AC = 0, the equation represents a parabola;
--> if B%5E2++-+4AC > 0, the equation represents a hyperbola;
**if we also have A + C = 0, the equation represents a rectangular hyperbola.