Cones

  • A cone is the set of all lines which pass through a curve and a fixed point. The fixed point does not lie in the plane of the curve. The fixed point is called the vertex and the fixed curve is called the base curve or the directrix of the cone.

  • Each line that make up the cone is called the generator of the cone.

  • Every planar section of a cone is a conic.

  • The equation of a cone whose base curve is a conic and whose vertex is (0, 0, 0) is a homogeneous equation of degree 2 in 3 variables.

  • If a cone ax2 + by2 + cz2 + 2fyx + 2gzx + 2hxy = 0 has three mutually perpendicular generators then a + b + c = 0.



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