Parabola problem help?

The reflector of a flashlight is in the shape of a paraboloid of revolution. Its diameter is 4 centimeters and its depth is 1 centimeter. How far from the vertex should the light bulb be placed so that the rays will be reflected parallel to the axis?

Comments

  • Diameter = 4 cm.

    Depth = 1 cm.

    The diameter of the parabola defines a point P(x, y) as:

    P(4, 0):

    x = 4

    y = 0

    Half the diameter defines the x-value of the vertex, h, as

    h = 1/2 x

    h = 1/2 (4)

    h = 2

    The depth, k, defines the y-value, k, of the vertex:

    k = 1

    Equation of Parabola:

    y = a (x - h)² + k:

    0 = a (4 - 2)² + 1

    0 = a (2)² + 1

    0 = a (4) + 1

    0 = 4a + 1

    4a = - 1

    a = - 1/4

    p = 1 / 4a:

    p = 1 / 4(- 1/4)

    p = 1 / - 1

    p = - 1

    The light bulb should be placed 1 cm. from the vertex.

     

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