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Conic sections

Circles, ellipses, parabolas and hyperbolas as equations and as surfaces sliced.

Slice a cone and you get a circle, an ellipse, a parabola or a hyperbola; algebraically they are the second-degree equations in x and y. Completing the square in each variable reveals the centre and shape. The 3D view draws z = the expression, whose level curve z = 0 is the conic.

Worked example: x^2 + y^2 - 25

Algebra · Expressions

Analyse x^2 + y^2 - 25

x^{2} + y^{2} - 25

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  1. x^{2} + y^{2} - 25

    An expression in x, y. Here is what it does.

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x^{2} + y^{2} - 25

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More in Precalculus

Complex numbersPolynomial functionsRational functionsSequences and seriesThe binomial theoremVectors