81. Whispering galleries: Due to their unique properties, ellipses are used in the construction of whispering galleries like those in St. Paul's Cathedral (London) and Statuary Hall in the U.S. Capitol. Regarding the latter, it is known that John Quincy Adams (1767-1848), while a member of the House of Representatives, situated his desk at a focal point of the elliptical ceiling, easily eavesdropping on the private conversations of other House members located near the other focal point. Suppose a whispering gallery was built using the equation 1² 1, with the dimensions in feet. (a) How tall is the ceiling at its highest point? (b) How wide is the gallery vertex to vertex? (c) How far from the base of the doors at either end, should a young couple stand so that one can clearly hear the other whispering, "I love you."? 2809 2025
81. Whispering galleries: Due to their unique properties, ellipses are used in the construction of whispering galleries like those in St. Paul's Cathedral (London) and Statuary Hall in the U.S. Capitol. Regarding the latter, it is known that John Quincy Adams (1767-1848), while a member of the House of Representatives, situated his desk at a focal point of the elliptical ceiling, easily eavesdropping on the private conversations of other House members located near the other focal point. Suppose a whispering gallery was built using the equation 1² 1, with the dimensions in feet. (a) How tall is the ceiling at its highest point? (b) How wide is the gallery vertex to vertex? (c) How far from the base of the doors at either end, should a young couple stand so that one can clearly hear the other whispering, "I love you."? 2809 2025
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:81. Whispering galleries: Due to their unique properties, ellipses are
used in the construction of whispering galleries like those in St.
Paul's Cathedral (London) and Statuary Hall in the U.S. Capitol.
Regarding the latter, it is known that John Quincy Adams
(1767-1848), while a member of the House of Representatives,
situated his desk at a focal point of the elliptical ceiling, easily
eavesdropping on the private conversations of other House
members located near the other focal point. Suppose a whispering gallery was built using the equation
1²
1.²
= 1, with the dimensions in feet. (a) How tall is the ceiling at its highest point? (b) How wide is
2809 2025
the gallery vertex to vertex? (c) How far from the base of the doors at either end, should a young couple stand so
that one can clearly hear the other whispering, "I love you."?
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