How do you know which conic section you are graphing when it is written in general form?

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How do you know which conic section you are graphing when it is written in general form?

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Answer 1 · 2014-10-19T15:39:22

A conic section in general form has the equation

$A x^{2} + B x + C y^{2} + D y + E = 0$ $Ax^2 + Bx + Cy^2 + Dy + E = 0$

when either $A$ $A$ or $C$ $C$ is missing (i.e $A = 0$ $A = 0$ or $C = 0$ $C = 0$ ), you're dealing with a parabola.

when $A$ $A$ and $C$ $C$ has the same signs, you're dealing with either an ellipse or a circle. If $A$ $A$ and $C$ $C$ have the same value, you're dealing with a circle. Otherwise, you're dealing with an ellipse

when $A$ $A$ and $C$ $C$ have different signs, you're dealing with a hyperbola

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How do you know which conic section you are graphing when it is written in general form?

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