This preview shows page 1. Sign up to view the full content.
Unformatted text preview: a2
25 − a2
a2 a2 = 25 − a2
= 25 − 25
16 Substituting all of our ﬁndings into the equation
25 2 (x − h)2
(y − k )2
= 1, yields our ﬁnal answer
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...
View Full Document