document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086817>Question 1086817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Some long-range navigation systems use hyperbolas to determine a ship’s position. Suppose the system<BR>\n" );
document.write( "imposes coordinates so that the location of a ship is in the first quadrant. A ship is located at the intersection of the hyperbolas with equations 25x^2 – 4y^2 = 100 and  36y^2 – x^2= 64 . Find the coordinates of the ship to the nearest hundredth of a unit.\r<BR>\n" );
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document.write( "a. (1.90, 4.28)<BR>\n" );
document.write( "b. (2.07, 1.38)<BR>\n" );
document.write( "c. (1.38, 2.07) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701121 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=701121\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the solution is selection b. (2.07,1.38)\r<BR>\n" );
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document.write( "you can solve it algebraically as follows:\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "25x^2 – 4y^2 = 100<BR>\n" );
document.write( "36y^2 – x^2 = 64\r<BR>\n" );
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document.write( "re-arrange the terms so that they line up like for like.\r<BR>\n" );
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document.write( "25x^2 - 4y^2 = 100<BR>\n" );
document.write( "-x^2 + 36y^2 = 64\r<BR>\n" );
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document.write( "multiply both sides of the second equation by 25 to get:\r<BR>\n" );
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document.write( "25x^2 - 4y^2 = 100<BR>\n" );
document.write( "-25x^2 + 900y^2 = 1600\r<BR>\n" );
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document.write( "add the equations together to get:\r<BR>\n" );
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document.write( "896y^2 = 1700\r<BR>\n" );
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document.write( "solve for y^2 to get:\r<BR>\n" );
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document.write( "y^2 = 1.897321429\r<BR>\n" );
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document.write( "solve for y to get:\r<BR>\n" );
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document.write( "y = plus or minus 1.377432913\r<BR>\n" );
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document.write( "since the intersection point has to be in the first quadrant, then you get:\r<BR>\n" );
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document.write( "y = plus 1.377432913\r<BR>\n" );
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document.write( "replace y^2 with 1.897321429 in the first equation to get:\r<BR>\n" );
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document.write( "25x^2 - 4 * 1.897321429 = 100\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "25x^2 - 7.589285714 = 100\r<BR>\n" );
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document.write( "add 7.589285714 to both sides of the equation to get:\r<BR>\n" );
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document.write( "25x^2 = 107.5892857\r<BR>\n" );
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document.write( "solve for x^2 to get:\r<BR>\n" );
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document.write( "x^2 = 107.5892857/25 = 4.303571429\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = plus or minus 2.074505104.\r<BR>\n" );
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document.write( "since x has to be in the first quadrant, then you get:\r<BR>\n" );
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document.write( "x = plus 2.074505104.\r<BR>\n" );
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document.write( "your intersection point in the first quadrant is:\r<BR>\n" );
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document.write( "(x,y) = (2.074505104,1.377432913)\r<BR>\n" );
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document.write( "round this to 2 decimal digits and you get:\r<BR>\n" );
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document.write( "(x,y) = (2.07,1.38)\r<BR>\n" );
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document.write( "that's selection b.\r<BR>\n" );
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document.write( "graphically, this looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/070601.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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