To calculate: The coordinates of the vertex of the hyperbolic mirror,
Answer to Problem 54E
The coordinates of the vertex of the hyperbolic mirror are
Explanation of Solution
Given information:
In the hyperbolic mirror provided below light ray directed at focus A is reflected to focus B .
Formula used:
The equation of horizontal hyperbola is
Calculation:
Consider the information that in the hyperbolic mirror provided below light ray directed at focus A is reflected to focus B .
Observe that it is in shape of hyperbola whose transverse axis is horizontal.
Recall that the equation of horizontal hyperbola is
Here center is origin so
The above relation is between a and b .
Also, the hyperbola passes through the point
Substitute x as 24, y as 243, b as
Factor and simplify the expression obtained above,
But since value of a cannot be greater than c so reject
Therefore, vertex of mirror when its mount at top of edge of mirror with coordinates
Thus, the coordinates of the vertex of the hyperbolic mirror are
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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