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Five Points Determine a Conic Section

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Five points determine a conic section. In this Demonstration, move up to six points, and see all the conic sections that pass through any subset of five points.

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Use Cmd+Click on Mac or Alt+Click on Windows to add or remove locators. If you hold the mouse over any curve, the equation of the corresponding conic is displayed.

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Contributed by: Ed Pegg Jr (April 2008)
Modified by: Paul Abbott
Open content licensed under CC BY-NC-SA

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Following MathWorld, the equation of the conic through the five points can be computed with the determinant

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