SOLUTION: How do I identify an equation if it is a circle, parabola, ellipse, or hyperbola?

Question 432360: How do I identify an equation if it is a circle, parabola, ellipse, or hyperbola?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
If the equation has both x^2 and y^2 terms with EQUAL coefficients, then it is probably a CIRCLE.

If the equation has both x^2 and y^2 terms with UNEQUAL coefficients but with the same SIGN, then it is probably an ELLIPSE.

If the equation has both x^2 and y^2 terms with OPPOSITE signs, then it is probably a HYPERBOLA.

If the equation has an x^2 term but NO y^2 term, or a y^2 term but NO x^2 term, then it probably a PARABOLA.

I say "probably", because there under certain other conditions, there may be exceptions in which the graph is a point or no solution.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

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