Quadratic Equation with three variables

[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

 

[phinds]

If you have 3 independent variables, is it still a quadratic equation?

 

[fresh_42]

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?

Eventually. E.g. http://www.wolframalpha.com/input/?i=x^2+5y^2-3z^2=7 and https://en.wikipedia.org/wiki/Quadric

 

[Mark44]

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.