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Conic Sections
The Parabola

 

Problem  1
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Consider the parabola with vertex at the origin defined by the equation \(y=\dfrac{1}{6}x^2\)

  1. Find the coordinates of the focus.

  2. Find the equations of the directrix and the axis of symmetry.

  3. Find the value(s) of \(a\) for which the point \((a,4)\) is on the parabola.

  4. Sketch the parabola, and indicate the focus and the directrix.

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Stephanie cc
Stephanie
Nathan cc
Nathan
Julieta cc espanol spanish
Julieta
Problem  2

Determine the equation in standard form of the parabola with vertex at the origin and directrix \(x=3\). Sketch the parabola, and indicate the focus and the directrix.

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Stephanie cc
Stephanie
Nathan cc
Nathan
Julieta cc espanol spanish
Julieta
Problem  3

Determine the equation in standard form of the parabola with directrix \(y=7\) and focus at \((-3,3)\). Sketch the parabola.

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Stephanie cc
Stephanie
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  4

Find the vertex and focus of the parabola \[-4x+3y^2+12y-8=0\] Determine the equation of the directrix and sketch the parabola.

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Stephanie cc
Stephanie
Breylor cc
Breylor
Problem  5

The cross-section of a headlight reflector is in the shape of a parabola. The reflector is \(6\) inches in diameter and \(5\) inches deep, as illustrated in Figure 15.

  1. Find an equation of the parabola, using the position of the vertex of the parabola as the origin of your coordinate system.

  2. The bulb for the headlight is positioned at the focus. Find the position of the bulb.

Choose instructor to watch:
Shelby cc
Shelby
Nathan cc
Nathan
Julieta cc espanol spanish
Julieta