Unformatted text preview: 1.9. For simplicity, we assume the hyperbola
is centered at (0, 0) with its foci at (−5, 0) and (5, 0). Schematically, we have 7.5 Hyperbolas 441
y
6
5
4
3
2
1 Jeﬀ −6 −5 −4 −3 −2 −1
−1 Carl
1 2 3 4 5 6 x −2
−3
−4
−5
−6 2 2 We are seeking a curve of the form x2 − y2 = 1 in which the distance from the center to each focus
a
b
is c = 5. As we saw in the derivation of the standard equation of the hyperbola, Equation 7.6,
d = 2a, so that 2a = 1.9, or a = 0.95 and a2 = 0.9025. All that remains is to ﬁnd b2 . To that end,
we recall that a2 + b2 = c2 so b2 = c2 − a2 = 25 − 0.9025 = 24.0975. Since Sasquatch is closer to
2
x2
Jeﬀ than it is to Carl, it must be on the western (left hand) branch of 0.9025 − 24.y
0975 = 1.
In our previous example, we did not have enough information to pin down the exact location of
Sasquatch. To accomplish this, we would need a third observer.
Example 7.5.5. By a stroke of luck, Kai was also camping in the woods during the events of the
previous example. He was located 6 miles due north of Jeﬀ and heard the Sa...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details