document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=886180>Question 886180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What's the equation of the hyperbola with a focus at (-3,sqrt13), asymptotes intersecting at (-3,1) and one asymptote passing through the point (1,7)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535746 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=535746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> as best i can determine, the equation of your hyperbola will be:<BR>\n" );
document.write( "(y-1)^2 / 9 - (x+3)^2 / 4 = 1\r<BR>\n" );
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document.write( "a^2 = 4<BR>\n" );
document.write( "b^2 = 9<BR>\n" );
document.write( "c^2 = 13<BR>\n" );
document.write( "this makes c = +/- sqrt(13)\r<BR>\n" );
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document.write( "as if this isn't confusing enough, some tutorials align the a with the axis line and the b with the line vertical to the axis line and you will see:\r<BR>\n" );
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document.write( "a^2 = 9<BR>\n" );
document.write( "b^2 = 4<BR>\n" );
document.write( "c^2 = 13\r<BR>\n" );
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document.write( "the net result is the same, however, with the equation of the hyperbola as shown above.\r<BR>\n" );
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document.write( "the center of the hyperbola is the intersection of the asymptotes which is at (-3,1)\r<BR>\n" );
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document.write( "the equation of the asymptotes is:\r<BR>\n" );
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document.write( "y = 3/2x + 11/2<BR>\n" );
document.write( "y = -3/2x - 7/2\r<BR>\n" );
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document.write( "the hyperbola will have vertex at (-3,4) and (-3,-2).<BR>\n" );
document.write( "this is because the sqrt(9) = 3 and that is the term under the (y-1)^2 term which is equal to the distance from the vertex to the center of the hyperbola.\r<BR>\n" );
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document.write( "the width of the hyperbola is equal to the center plus or minus 2 parallel to the x-axis.\r<BR>\n" );
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document.write( "the foci of the hyperbola will be at (-3,1+sqrt(13)) and (-3,1-sqrt(13)).\r<BR>\n" );
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document.write( "that puts them at about (-3,4.6) and (-3,-2.6) \r<BR>\n" );
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document.write( "those focus points are just beyond the vertex points of (-3,4) and (-3,-2)\r<BR>\n" );
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document.write( "the eccentricity is equal to c/b or c/a, whichever the case may be.<BR>\n" );
document.write( "in this problem it is equal to sqrt(13) / 3 which is equal to 1.2 roughly.\r<BR>\n" );
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document.write( "the graph of the hyperbola is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/jul0802.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "here's a couple of links that talk about hyperbolas.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://tutorial.math.lamar.edu/Classes/Alg/Hyperbolas.aspx\" target = \"_blank\">http://tutorial.math.lamar.edu/Classes/Alg/Hyperbolas.aspx</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/hyperbola.htm\" target = \"_blank\">http://www.purplemath.com/modules/hyperbola.htm</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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