(a)
To find : An equation for the mirror.
The required equation is
Given information :
A hyperbolic mirror reflects light directed toward one focus to the other focus. The hyperbolic mirror shown has foci at
Explanation :
Consider the figure.
The vertices are
The foci are at
Now,
Therefore, the required equation is
(b)
To find : An equation for the path of light beam originating at the point
The required equation is
Given information :
A hyperbolic mirror reflects light directed toward one focus to the other focus. The hyperbolic mirror shown has foci at
Explanation :
The slope of the line joining
So, the equation of the line originating at
Therefore, the required equation is
(c)
To calculate : The point at which light beam originating at the point
The light beam originating at the point
Given information :
A hyperbolic mirror reflects light directed toward one focus to the other focus. The hyperbolic mirror shown has foci at
Calculation :
The equation for the path of light beam originating at the point
So,
Substitute the value of
Use quadratic formula,
Now, substitute the value of
Therefore, the light beam originating at the point
Chapter 8 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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