B Quadratic Equation with three variables

  • Thread starter Leo Authersh
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Leo Authersh

If a quadratic equation of two variables represents a conic section (planar intersection of a cone), then does a quadratic equation of three variables represent the complete cone?

@fresh_42 @FactChecker @WWGD
 
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If you have 3 independent variables, is it still a quadratic equation?
 

fresh_42

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If a quadratic equation of two variables represents a conic section (planar intersection of a cone), then does a quadratic equation of three variables represent the complete cone?
No.
The usual terminology is second-degree equation. As already mentioned, a second-degree equation in three variables represents a quadric surface, including spheres, ellipsoids, paraboloids, hyperboloids, cones, and a few other degenerate surfaces (the equation ##x^2 + y^2 + z^2 = 0## represents a single point at the origin.)

@Leo Authersh, please do a little basic research before posting your questions. Also, I have moved several of your threads to the General Math section. They are not questions that pertain to Topology or Analysis.
 

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