Abstract:

         This paper addresses the orbit equation ∑′ passing a fixed point and the midpoint in the secant of a fixed quadratic surface and the orbit equation ∑″ of a point dividing a line segment in a given ratio between a fixed point and a moving point of a quadratic surface. This paper further presents such orbit equations as ∑′ and ∑″ for seventeen quadratic surfaces and derives two important conclusions for typepreserving of quadratic surfaces.

Key words: quadratic surface, typepreserving, typepreserving transformation