Answer to Question #124582 in Analytic Geometry for Samuel kassapa

Question #124582
A statuary hall is elliptical in shape. It measures 42 feet wide and 96 feet long. If a person is standing at one focus, her whisper can be heard by a person standing at the other focus. How far apart are the two people
1
Expert's answer
2020-07-01T19:00:26-0400



As per the question the elliptical shaped statuary hall has been drawn which is 96 ft long and 48 ft

wide. Let us assume that the person is standing at focus F1 and her whisper can be heard by a person standing at another focus F2.


This a typical ellipse with major axis 96 ft and Minor axis 42 ft following standard equation of ellipse which is "\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1."


Here "a= 48 \\space and \\space b=21\\\\\\therefore eccenticity (e) = \\sqrt{1-\\frac{b^2}{a^2}}"


"Now \\space e = \\sqrt{1-\\frac{21^2}{48^2}}\\\\or, e=\\sqrt{1-\\frac{441}{2304}}\\\\or, e=\\sqrt{\\frac{2304-441}{2304}}\\\\or, e=\\sqrt{\\frac{1863}{2304}}\\\\or, e=\\frac{\\sqrt{1863}}{48}\\\\or, e=\\frac{43.16}{48}\\\\or, e = 0.899 \\\\or, e = 0.9"


now the distance between the foci F1 and F2 is F1F2 "=2ae."

"\\therefore 2ae = 2*48*0.9"

"=" "86.4 \\space ft."


"\\therefore" The two persons are 86.4 ft apart. (Answer)




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