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To find: How deep should the mirror be in order to reflect the light rays parallel to the axis of symmetry.
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Answer to Problem 39RE
Depth of the mirror should be feet or 3 inches.
Explanation of Solution
Given:
A searchlight is shaped like a paraboloid of revolution. If a light source is located 1 foot from the vertex along the axis of symmetry and the opening is 2 feet across.
Calculation:
Let be the vertex of the parabola and let it open up.
The equation of the parabola is .
The light source is located 1 foot from the vertex along the axis of symmetry.
Therefore, .
Hence, the equation is .
The width of opening is 2 so that is located on the parabola.
Substituting in , we get,
,
feet
The mirror is feet, or 3 inches.
Chapter 10 Solutions
Precalculus Enhanced with Graphing Utilities
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