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B Quadratic Equation with three variables

  1. Sep 11, 2017 #1
    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
  2. jcsd
  3. Sep 11, 2017 #2


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    If you have 3 independent variables, is it still a quadratic equation?
  4. Sep 11, 2017 #3


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    Staff: Mentor

  5. Sep 12, 2017 #4


    Staff: Mentor

    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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