Stitz-Zeager_College_Algebra_e-book

# 6 not surprisingly a system with more variables than

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Unformatted text preview: a2 4= √ 2 = 25 − a2 25 16 a2 a2 = 25 − a2 = 25 − 25 16 = 375 16 Substituting all of our ﬁndings into the equation 16x2 y2 + = 1. 375 25 2 (x − h)2 (y − k )2 + = 1, yields our ﬁnal answer a2 b2 As with parabolas, ellipses have a reﬂective property. If we imagine the dashed lines below as sound waves, then the waves emanating from one focus reﬂect oﬀ the top of the ellipse and head towards the other focus. Such geometry is exploited in the construction of so-called ‘Whispering Galleries’. If a person whispers at one focus, a person standing at the other focus will hear the ﬁrst person as if they were standing right next to them. 7.4 Ellipses 427 F1 F2 Example 7.4.5. Jamie and Jason want to exchange secrets (terrible secrets) from across a crowded whispering gallery. Recall that a whispering gallery is a room which, in cross section, is half of an ellipse. If the room is 40 feet high at the center and 100 feet wide at the ﬂoor, how far from the outer wall should each of them stand so that...
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## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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