document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982303>Question 982303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation in standard form for the hyperbola with vertices at (0, +/-10) and asymptotes at<BR>\n" );
document.write( "y = +/- 5/4 x\r<BR>\n" );
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document.write( "My work, can someone please double check it?<BR>\n" );
document.write( "Given: a = 10 <BR>\n" );
document.write( "The relationship between a, b, and c is <BR>\n" );
document.write( "10² + b² = c² \r<BR>\n" );
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document.write( "The slope of the asymptotes is ±5/4 <BR>\n" );
document.write( "a = is a multiple of 5 <BR>\n" );
document.write( "b = is a multiple of 4 <BR>\n" );
document.write( "For this problem a = 10 <BR>\n" );
document.write( "hence, b = 8 \r<BR>\n" );
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document.write( "10² + 8² = c² <BR>\n" );
document.write( "164 = c² <BR>\n" );
document.write( "2&#8730;41 = c \r<BR>\n" );
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document.write( "Summary <BR>\n" );
document.write( "center = (0, 0) <BR>\n" );
document.write( "a² = 100 <BR>\n" );
document.write( "b² = 64 <BR>\n" );
document.write( "c² = 164 <BR>\n" );
document.write( "transverse axis x = 0 <BR>\n" );
document.write( "equation of the hyperbola \r<BR>\n" );
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document.write( "[y²/10²] - [x²/8²] = 1  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603141 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=603141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "No.   a is 10 because the vertices are (0,-10) and (0,10), not because it is a multiple of 5.\r<BR>\n" );
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document.write( "But the slopes of the asymptotes are <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \pm\frac{b}{a}\"> for any hyperbola and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \pm\frac{5}{4}\">.  a is a multiple of 4, not 5.  b is a multiple of 5.\r<BR>\n" );
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document.write( "Like I said before, solve for b\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{b}{10}\ =\ \frac{5}{4}\">\r<BR>\n" );
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document.write( "Cross multiply:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  4b\ =\ 50\">\r<BR>\n" );
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document.write( "You can take it from here.  Hint, just because every other example you have ever seen have a and b as integers, doesn't mean every hyperbola is that way.  a and b can be any real numbers, they don't even have to be rational.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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