SOLUTION: Two radar sites are tracking a jetfighter. The first radar is located at (0,0) and shows a jetfighter to be 300 kilometers away. The second radar site, is located 250 kilometers

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Question 1199588: Two radar sites are tracking a jetfighter. The first radar is located at
(0,0) and shows a jetfighter to be 300 kilometers away. The second
radar site, is located 250 kilometers east of the first radar. The
second radar detects the jet fighter 120 kilometers away from it.
Find the coordinates of ALL possible points where the jetfighter
could be located. Determine the equation of the hyperbola where
the jetfighter could be located. Make a clear illustration to support
your answer.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Two radar sites are tracking a jetfighter. The first radar is located at
(0,0) and shows a jetfighter to be 300 kilometers away. The second
radar site, is located 250 kilometers east of the first radar. The
second radar detects the jet fighter 120 kilometers away from it.
Find the coordinates of ALL possible points where the jetfighter
could be located. Determine the equation of the hyperbola where
the jetfighter could be located. Make a clear illustration to support
your answer.
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From the info about the first radar, we have this equation

    x%5E2 + y%5E2 = 300%5E2.                 (1)


From the info about the second radar, we have this equation
 
    %28x-250%29%5E2 + y%5E2 = 120%5E2.          (2)


In the expanded form, the system of equations is

    x^2                + y^2 = 300^2    (3)

    x^2 - 500x + 250^2 + y^2 = 120^2    (4)


We should solve these two equations simultaneousdly.

For it, subtract equation (4) from equation (3).  You will get


          500x - 250^2 = 300^2 - 120^2

          500x = 300^2 - 120^2 + 250^2

          500x = 138100

             x = 138100/500 = 276.2.


Then from equation (1)

          y%5E2 = 300%5E2 - 276.2%5E2 = 13713.56

          y = +/- sqrt%2813713.56%29 = +/- 117.105  (rounded)


ANSWER.  The possible coordinates of the jetfighter are  (276.200,117.105)  OR  (276.200,-117.105), in kilometers.

Solved.

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The question about a hyperbola is  highlight%28highlight%28IRRELEVANT%29%29  to this problem
and could arise in this post only as a result of a fatal  highlight%28highlight%28MISTAKE%29%29  of the writer.