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Conic Section Formulas - Problem 3


Most of the work that we do with conics is from standard form with squared binomials, but we can still tell what type of conic we're presented with from an equation in general form. If only one variable is squared, then you know for sure you have a parabola. If both variables are squared, then you must discern between an ellipse, hyperbola, or circle: first, get the squared terms on the same side of the equals sign. If they have the same coefficients and are added, then it's a circle; if they have different coefficients and are added, then it's an ellipse; and if they are subtracted, it's a hyperbola. You would need to complete the square to know any more details about key features.

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