document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=450304>Question 450304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the length of the transverse axis of the hyperbola defined by the equation below? (y-6)^2/6^2-(x+5)^2/12^2=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #309852 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=309852\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the length of the transverse axis of the hyperbola defined by the equation below\r<BR>\n" );
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document.write( " (y-6)^2/6^2-(x+5)^2/12^2=1<BR>\n" );
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document.write( "Standard form of hyperbola with horizontal transverse axis:  (x-h)^2/a^2-(y-k)^2/b^2=1,<BR>\n" );
document.write( "with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "Standard form of hyperbola with vertical transverse axis:  (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "The difference between these two forms is that the (x-h)^2 and (y-k)^2 terms are interchanged.<BR>\n" );
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document.write( "Given equation of hyperbola: (y-6)^2/6^2-(x+5)^2/12^2=1<BR>\n" );
document.write( "This is a hyperbola of the 2nd form listed. It has a vertical transverse axis with center at (-5,6).<BR>\n" );
document.write( "a^2=6^2<BR>\n" );
document.write( "a=6=distance from center to vertex<BR>\n" );
document.write( "Length of transverse axis=distance between vertices=2a=12<BR>\n" );
document.write( "See the graph below for visual evidence of the algebra above:\r<BR>\n" );
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document.write( "y=(36(1+(x+5)^2/144))^.5+6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-50%2C+50%2C+-50%2C+50%2C%2836%281%2B%28x%2B5%29%5E2%2F144%29%29%5E.5%2B6%2C%0D%0A-%2836%281%2B%28x%2B5%29%5E2%2F144%29%29%5E.5%2B6%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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