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Unformatted text preview: after Jeﬀ, so Kai is farther from Sasquatch than Jeﬀ. Thus Sasquatch must lie on
the southern branch of the hyperbola (y3−3) − (x+5) = 1. Looking at the western branch of the
hyperbola determined by Jeﬀ and Carl along with the southern branch of the hyperbola determined
by Kai and Jeﬀ, we see that there is exactly one point in common, and this is where Sasquatch
must have been when it called.
y Kai 6
2 Jeﬀ 1 −9 −8 −7 −6 −5 −4 −3 −2 −1
−1 Sasquatch Carl
1 2 3 4 5 6 x −2
−6 To determine the coordinates of this point of intersection exactly, we would need techniques for
solving systems of non-linear equations. We will see those later in Section 8.7. A calculator can 7.5 Hyperbolas 443 be of use in approximating these coordinates using the Intersect command. In order to use this
command, however, we ﬁrst need to solve each of our hyperbolas for y , choose the correct equation
to enter into the calculator, and proceed from there. We leave this as an exercise.
The procedure outlined in the two previous examples is the basis for LOng Range Aid to Navigation
(LORAN for short.) While it appears to be losing its popularity due to Global Positioning Satellites
(GPS), it remains one of most important applications of hyperbolas. 444 7.5.1 Hooked on Conics Exercises 1. Graph the hyperbola. Find the center, the lines which contain the transverse and conjugate
axes, the vertices, the foci and the equations of the asy...
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