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7.3_bzca5e

# 7.3_bzca5e - Example A student scientist wants to construct...

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Section 7.3 The Parabola

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Definition of a Parabola

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Example 2 Find the vertex and the axis of symmetry of the parabola given by y 2( 3) 4. Does it open up or down? x = - -

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Standard Form of the Equation of a Parabola

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Example 2 Find the focus and the directrix of the parabola given by y 24 . x =
Using the Standard Form of the Equation of a Parabola

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Example 2 Find the focus and the directrix of the parabola given by x 4 . y = -

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Example 2 Find the focus and the directrix of the parabola given by y 12 . x = -
Translations of Parabola

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Example Find the standard form of the equation of a parabola with focus (0,3) and directrix of y=-1
Example 2 Find the vertex, focus and directrix of the parabola given by (x-3) 8( 1). y = +

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Example 2 Find the vertex, axis, focus, and directrix of the parabola by completing the square on the equation 8y=2x 12 14. x - -
Example 2 Find the vertex, axis, focus, and directrix of the parabola by completing the square on the equation 6 16 25 0. y y x - + + =

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Applications
Applications of Parabolas- cables on suspension bridges, arches on bridges, solar cookers, reflectors on lights, satellite dishes

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Unformatted text preview: Example A student scientist wants to construct a solar cooker which is in the shape of a parabolic dish with a diameter of 6 feet and a depth of 1 foot. Where should the cooker (focus) be located to get the maximum reflected sun rays to cook the food. 6 feet 1 foot (3,1) (0,0) cooker Degenerate Conic Sections Intersections might now result in a conic section. Three degenerate cases occur when the cutting plane passes through the vertex. These degenerate conic sections are a point, line, and a pair of intersecting lines. (a) (b) (c) (d) 2 Find the focus and directrix of the parabola with the given equation. y 16 . x = ( 4,0), 4 (4,0), 4 (4,0), 4 (0,4), 4 y x y x-= -= -= = (a) (b) (c) (d) 2 Find the vertex of the following parabola (x+4) 12( 2). y = + (2,4) (4,2) ( 4, 2) ( 2, 4)- -- -(a) (b) (c) (d) 2 Find the focus of the following parabola (x+4) 12( 2). y = + (2, 4) (4,1) ( 4, 2) ( 4,1)-- --...
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7.3_bzca5e - Example A student scientist wants to construct...

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