document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068652>Question 1068652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I've got two LORAN stations A and B that are 500 miles apart. A and B are also the Foci of a hyperbola. A ship at point P (which lies on the hyperbola branch with A as the focus) receives a nav signal from station A 2640 micro-sec before it receives from B. If the signal travels 980 ft/microsecond, how far away is P from A and B? Also, what are the values for a, b, and c? Show your illustration. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683917 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=683917\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The difference in the distances from any point on a hyperbole to the foci is a constant - by convention the first distance is to the furthest focus<BR>\n" );
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document.write( "(a + c) – (c – a) = 2a<BR>\n" );
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document.write( "the distance from the center to either focus is c = 250 miles<BR>\n" );
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document.write( "we can place the center of the hyperbole at the origin of its graph - this means we have h = k = 0<BR>\n" );
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document.write( "2a = 2640 * 980 = 2587200<BR>\n" );
document.write( "a = 1293600 ft = 1293600 / 5280 = 245 miles<BR>\n" );
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document.write( "for hyperbola's b^2 = c^2 - a^2<BR>\n" );
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document.write( "b^2 = 250^2 - 245^2 = 2475<BR>\n" );
document.write( "b = 49.74937 approximately 49.75<BR>\n" );
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document.write( "distance from P to A is c - a = 250 - 245 = 5 miles<BR>\n" );
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document.write( "distance from P to B is c + a = 250 + 245 = 495 miles<BR>\n" );
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document.write( "a = 245 miles<BR>\n" );
document.write( "b = 49.75 miles<BR>\n" );
document.write( "c = 250 miles<BR>\n" );
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