To find: The where should light hit the mirror so that light will be reflected to
Answer to Problem 51SGR
The light sourceshould hit the mirror at point
Explanation of Solution
Given information:
Light source
Light will be reflected to
Calculation:
Consider a hyperbolic mirror which is modeled by the upper branch of the hyperbola
The mirror reflects light rays directed at one focus towards the other focus.
Compare equation (1)
Use relation between a, b and c and compute the value of c as follows,
Hence, foci of the given hyperbola will be
A light source located at
Compute the equation of the path of the light source using equation of line passing through two points
Compute the intersection point of hyperbola (1)
Substitute
Use quadratic formula,
For
For
So, intersection points of given hyperbola and the path of light source are
The point
Therefore, the light sourceshould hit the mirror at point
Chapter 9 Solutions
Glencoe Algebra 2 Student Edition C2014
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