6.1 - Conic Sections

6.1 - Conic Sections - Name_ 6.1: Conic Sections PARABOLA A...

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Name___________________________________ 6.1: Conic Sections P ARABOLA A parabola is the set of points in the plane that are equidistant from a fixed line (the directrix ) and a fixed point (the focus ) not on the directrix. The midpoint of the line segment between the focus and the directrix on the axis of symmetry is the vertex . x y Vertex Focus Directrix Axis of symmetry x y Axis of symmetry Vertex Focus Directrix Example. Find the focus and directrix of the parabola given by the equation: x = 4 y 2 Solution. x = 4 y 2 y 2 = 1 4 x ∆ Rearrange into one of the four standard forms. y 2 = 4 px y 2 = 4 ? ? x y 2 = 4 1 16 x because y 2 = 4 1 16 x = 1 4 x So, p = 1 16 Focus: 1 16 , 0 Directrix: x = - 1 16 . x 1 y 1 (1, .5) (1, -.5) NOTE: one x is associated with two y 's
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Example. Find the focus and directrix of the parabola given by the equation: y = - 1 3 x 2 Solution. y = - 1 3 x 2 x 2 = -3 y ∆ Rearrange into one of the four standard forms. x 2 = 4 py x 2 = 4 ? ? y x 2 = 4 -3 4 x because x 2 = 4 -3 4 y = -3 y So, p = -3 4 Focus: 0, -3 4 Directrix: y = 3 4 .
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This note was uploaded on 04/13/2008 for the course MATH 2412 taught by Professor Matroy during the Spring '08 term at Alamo Colleges.

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6.1 - Conic Sections - Name_ 6.1: Conic Sections PARABOLA A...

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