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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