SOLUTION: A conference room is shaped like semi-elliptic arch. The height of the arch is 5m and its width is 16m. A. Where should two friends stand so that they can clearly hear each othe

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A conference room is shaped like semi-elliptic arch. The height of the arch is 5m and its width is 16m. A. Where should two friends stand so that they can clearly hear each othe      Log On


   

Question 1121022: A conference room is shaped like semi-elliptic arch. The height of the arch is 5m and its width is 16m.
A. Where should two friends stand so that they can clearly hear each other?
B. How far from the center of the room should two friends stand?
Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.
According to the condition, the ellipse (or semi-ellipse)  semi-minor and semi-major axes are 5 m and 16/2 = 8 m, respectively.


Hence, the linear eccentricity is  sqrt%288%5E2-5%5E2%29 = 6.245 m.


It is the distance from the center of the semi-ellipse to its focuses.



Answer.  The two friends should stay at the focuses of the ellipse that are located at the distance of 6.245 m from the center of the ellipse.

P.S.   To be exactly precise,  the two friends should  LIE  on the floor at that locations to have their mouths and their ears
maximally close to the focuses :-).

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For relevant lessons,  see
    - Ellipse definition, canonical equation, characteristic points and elements
    - Ellipse focal property
    - Tangent lines and normal vectors to a circle
    - Tangent lines and normal vectors to an ellipse
    - Optical property of an ellipse
    - Optical property of an ellipse revisited

    - Practical problems from the archive related to ellipses and parabolas


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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Comment from student :   Thank you so much maam.  How about the letter  B?


My response :   I answered both questions.  Read my answer attentively . . .