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Description
In the first part of this programme it is proved that a section of a cone is an ellipse. In the second part the different conic-sections, obtained when a plane is rotated through a cone, are discussed.
Module code and title: M101, Mathematics: a foundation course M101; 18 09-07-1978 1978 00:24:30 + Show more... Jack Koumi Norman Gowar; John Mason BBC Open University Ellipse; Directrix; Focus; Parabola; Hyperbola; Conics John Mason introduces the programme and looks at the geometric properties of an ellipse. He then moves on to examine an ellipse as created by a cone sliced by a plane. Norman Gowar proves that this is an ellipse by using two spheres which touch both the cone and the plane. The two focus points of the ellipse occur where the spheres contact the plane John Mason now examines what happens as the plane is moved through the cone, and as the cone is moved across the plane. The latter is demonstrated by shining a torch at different angles. With the aid of computer animations John and Norman examine the resulting sectional shapes as the plane is tilted through the cone. They obtain a parabola, a circle and a hyperbola. By tilting from the horizontal through to the vertical they cover all possible cases. These positions are shown again on the computer. John Mason then redefines the conies to fully integrate the parabola into the sequence. Norman Gowar demonstrates how this description is arrived at. All the conics are described in terms of their eccentricity, the distance to the focus divided by the distance to the directrix. 6HT/72532 00525_4256 2474 no