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**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...

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