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Surfaces of rotationLet some curve located in the plane The set of points of which the coordinates satisfy the equation Example. The following surfaces are surfaces of rotation:
Example. Find an equation of the surface obtained at rotating the line Solution: The surface of rotation is the cone with the vertex in the point
Let an orthonormal system of coordinates where the numbers Theorem. For every surface of the second order there is an orthonormal system of coordinates
where
Ellipsoid A surface given in some orthonormal system of coordinates by canonic equation of the form
Properties of an ellipsoid: 1. An ellipsoid is a restricted surface since from its canonic equation follows that 2. An ellipsoid has central symmetry regarding to the origin of coordinates; axial symmetry regarding the coordinate axes; planar symmetry regarding to the coordinate planes. 3. At cutting an ellipsoid by a plane that is orthogonal to any of the coordinate axes an ellipse is obtained. For example, considering the cutting plane
Date: 2015-12-18; view: 1413
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