Math 41 Sections 11.1 and 11.2 - 11.1 Conics the word conic...

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11.1 Conics - the word conic derives from the word cone. A cone has a fixed line called an axis , a vertex , generators, and the two parts(sides) of the cone are called nappes . - conics , an abbreviation for conic sections , are curves that result from the intersection of a right circular cone and a plane. Circles are made when a plane is perpendicular to the axis of the cone and intersects each generator, but intersects only one nappe of the cone; parabolas when the plane is tilted farther so that it is parallel to one generator and intersects only one nappe of the cone; and hyperbolas when the plane intersects both nappes. Degenerate Conics – if the plane does not contain the vertex, it is the intersection of the plane and the cone is a point, a line, or a pair of intersection lines. 11.2 The Parabola - a parabola is the collection of all points P in the plane that are the same distance from a fixed point F as they are from a fixed line D. The point F is called the focus of the parabola, and the line D is its
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