Algebra.Com's Answer #833536 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Two radar sites are tracking a jetfighter. The first radar is located at
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document.write( "(0,0) and shows a jetfighter to be 300 kilometers away. The second
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document.write( "radar site, is located 250 kilometers east of the first radar. The
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document.write( "second radar detects the jet fighter 120 kilometers away from it.
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document.write( "Find the coordinates of ALL possible points where the jetfighter
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document.write( "could be located. Determine the equation of the hyperbola where
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document.write( "the jetfighter could be located. Make a clear illustration to support
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document.write( "your answer.
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document.write( "From the info about the first radar, we have this equation\r\n" );
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document.write( "  +  =  . (1)\r\n" );
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document.write( "From the info about the second radar, we have this equation\r\n" );
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document.write( "  + =  . (2)\r\n" );
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document.write( "In the expanded form, the system of equations is\r\n" );
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document.write( " x^2 + y^2 = 300^2 (3)\r\n" );
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document.write( " x^2 - 500x + 250^2 + y^2 = 120^2 (4)\r\n" );
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document.write( "We should solve these two equations simultaneousdly.\r\n" );
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document.write( "For it, subtract equation (4) from equation (3). You will get\r\n" );
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document.write( " 500x - 250^2 = 300^2 - 120^2\r\n" );
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document.write( " 500x = 300^2 - 120^2 + 250^2\r\n" );
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document.write( " 500x = 138100\r\n" );
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document.write( " x = 138100/500 = 276.2.\r\n" );
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document.write( "Then from equation (1)\r\n" );
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document.write( " = -  = 13713.56\r\n" );
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document.write( " y = +/-  = +/- 117.105 (rounded)\r\n" );
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document.write( "ANSWER. The possible coordinates of the jetfighter are (276.200,117.105) OR (276.200,-117.105), in kilometers.\r\n" );
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document.write( "Solved.\r
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document.write( "The question about a hyperbola is  to this problem
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document.write( "and could arise in this post only as a result of a fatal  of the writer.\r
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