SOLUTION: The path of aship can be described by a hyperbolic model centered at the origin, relative to two stations on the shore 168 miles apart that are located at the foci. If the ship is

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Question 1198028: The path of aship can be described by a hyperbolic model centered at the origin, relative to two stations on the shore 168 miles apart that are located at the foci. If the ship is 60 miles south of the center of the hyperbola, find the equation of the hyperbola.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
two stations on the shore 168 miles apart that are located at the foci

so, the coordinates of focus will be F(84,0) and F(-84,0) => c=84
enter is at origin =>h=0+ and k=0
the ship is 60 miles south of the center of the hyperbola=> b=60%0D%0A%0D%0Athen%0D%0A%0D%0A%7B%7B%7Bc%5E2=a%5E2%2Bb%5E2
84%5E2=a%5E2%2B60%5E2
a%5E2=84%5E2-60%5E2
a%5E2=3456
a=sqrt%283456%29
a=24sqrt%286%29


The general equation of hyperbola you need is:
x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1
So, the equation of path of ship which is in the form of hyperbola is
x%5E2%2F%2824sqrt%286%29%29%5E2-y%5E2%2F60%5E2=1
x%5E2%2F3456-y%5E2%2F3600=1