SOLUTION: A whispering gallery allows a whisper in one area to be heard plainly in a second area. A whispering gallery with an elliptical shape is built so that the person standing at one fo

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Question 1201817: A whispering gallery allows a whisper in one area to be heard plainly in a second area. A whispering gallery with an elliptical shape is built so that the person standing at one focus of the ellipse can whisper and be heard by another person standing at the other focus. The gallery will be 150 feet in length and 42 in width. A view from above is shown in the diagram.
a. What is the equation of the ellipse used to represent the outline of the room?
b. If two secret keepers are standing at the foci of the room to hear each other whisper, how far apart are they? Round to the nearest foot.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

Diagram should show an ellipse with the major axis of 150 feet and minor axis of 42 feet.


Then the major semi-axis is  150/2 = 75 ft and the minor semi-axis is 42/2 = 21 ft.


The standard equation of this ellipse is

     +  = 1.


The linear eccentricity of this ellipse is

    c =  = 72 ft.


The distance between the focuses of the ellipse is two times this value, i.e. 144 ft.

Solved.

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About this subject,  see the lesson
    - Ellipse definition, canonical equation, characteristic points and elements
in this site.



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