Multiple Conics Passing Through Four Points

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This applet demonstrates that, in general, two (distinct, nondegenerate) conic sections intersect in four points. Therefore, four points do not uniquely determine a conic section. Two different conic sections are drawn through the points A, B, C, and D. One of these conics passes through P₁; the other passes through P₂.

In the applet, you may click and drag the points A, B, C, and D; conics will be drawn passing through these points as described above. (The points P₁ and P₂ are stationary.)

Bradley and Stemkoski, Created with GeoGebra