Any point A(x, y, z) on the conical surface 2 1 13 is projected to the Z axis, and the vertical foot B(0, 0, z). △AOB is a right triangle, ∠ ABO = 90, ∠BAO=α.

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, cone, elliptic paraboloid and elliptic cylinder all have circular sections. If a plane 526 1 cuts the quadric surface on the circle, then all planes parallel to it also cut the surface on the circle.

Extended data:

Lateral area of the cone: The side of the cone spreads along the generatrix and is a sector. The arc length of this sector is equal to the circumference of the bottom of the cone, and the radius of the sector is equal to the length of the generatrix of the cone. The lateral area of the cone is arc length, and the circumference of the cone bottom × bus/2; It is a surface when it is not expanded.

A cone has a bottom surface, a side surface, a vertex, a height, and countless generatrixes. The development diagram of the bottom surface is a circle, and the development diagram of the side surface is a fan.

In life, sand piles, funnels, hats, gyroscopes, hats, pencil heads, drills, plumbs, etc. Can be approximately regarded as a cone. Sweet cones are also indispensable in daily life.