Tan ∠ Bao = tan α = ob/ab = | z |/√ (x 2+y 2), so the equation of the cone is: z 2 = (tan α) 2 (x 2+y 2).

In quadric surface, elliptic surface, hyperboloid, conical surface, elliptic paraboloid and elliptic cylinder all have circular section lines. If a plane cuts a quadric surface on a circle, all planes parallel to it also cut the surface on the circle. Therefore, in general, a quadric surface can be cut by two parallel planes. The tangent point of the tangent plane parallel to it is the umbilical point (or point) of the quadric surface.

Generally speaking, a straight line intersects a quadric surface at two points; If it intersects with more than three points, then all the lines are on the surface. This line is called the generatrix of the surface. If a quadric surface is cut by a parallel plane, then its section line is a quadric curve. Usually, we call the surface represented by the ternary quadratic equation quadric surface. A plane is called a quadric surface.

Quadratic surface is the general name of all the graphs corresponding to the ternary quadratic algebraic equation in the three-dimensional coordinate system (x, y, z). A surface expressed by quadratic equation (with real coefficient and non-zero quadratic coefficient) between coordinates x, y, z, y and z in Euclidean three-dimensional space. The equation of quadric surface is:

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