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

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 Algebra: Conic sections - ellipse, parabola, hyperbola Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Quadratic-relations-and-conic-sections Question 432360: How do I identify an equation if it is a circle, parabola, ellipse, or hyperbola?Answer by rapaljer(4667)   (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