Answer to Question #103611 in Analytic Geometry for aa

Question

x^2 +y^2 +z^2 = xyz is the equation of a cone.Is it true or false?

Answer 1

A cone is a quadric surface. The general equation of a quadtic equation is

$Ax² + By² + Cz² + 2Fxy + 2Gyz + 2Hzx + 2Px + 2Qy + 2Rz + D = 0$

The degree of this equation is 2.

The degree of the given equation $x^2 +y^2 +z^2 = xyz$ is 3. Therefore, this equation is not the equation of a cone.

Answer: False