document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982534>Question 982534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this problem? The equation of a hyperbola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2+-+x%5E2+%2B+8y+-+6x+-+41+=+0. ALIGN=MIDDLE  ALT=\"4y%5E2+-+x%5E2+%2B+8y+-+6x+-+41+=+0.\"   DISABLED_style= \"max-width:90%; height:auto;\" > Write the equation of the hyperbola in standard form and find the coordinates of the center, the coordinates of the vertices, and the equation of the asymptotes. Then graph the hyperbola. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603422 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=603422\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2+-+x%5E2+%2B+8y+-+6x+-+41+=+0 ALIGN=MIDDLE  ALT=\"4y%5E2+-+x%5E2+%2B+8y+-+6x+-+41+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y%5E2+%2B+8y%29-+%28x%5E2+%2B+6x%29+-41+=+0 ALIGN=MIDDLE  ALT=\"%284y%5E2+%2B+8y%29-+%28x%5E2+%2B+6x%29+-41+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y%5E2+%2B+2y%2Bb%5E2%29-4b%5E2+-%28x%5E2+%2B+6x%2Bb%5E2%29-%28-b%5E2%29+-41+=+0 ALIGN=MIDDLE  ALT=\"4%28y%5E2+%2B+2y%2Bb%5E2%29-4b%5E2+-%28x%5E2+%2B+6x%2Bb%5E2%29-%28-b%5E2%29+-41+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y%5E2+%2B+2y%2B1%5E2%29-4%2A1%5E2+-%28x%5E2+%2B+6x%2B3%5E2%29%2B3%5E2+-41+=+0 ALIGN=MIDDLE  ALT=\"4%28y%5E2+%2B+2y%2B1%5E2%29-4%2A1%5E2+-%28x%5E2+%2B+6x%2B3%5E2%29%2B3%5E2+-41+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y+%2B+1%29%5E2-4+-%28x+%2B+3%29%5E2%2B9+-41+=+0 ALIGN=MIDDLE  ALT=\"4%28y+%2B+1%29%5E2-4+-%28x+%2B+3%29%5E2%2B9+-41+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y+%2B+1%29%5E2-+%28x+%2B+3%29%5E2+-36+=+0 ALIGN=MIDDLE  ALT=\"4%28y+%2B+1%29%5E2-+%28x+%2B+3%29%5E2+-36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y+%2B+1%29%5E2-+%28x+%2B+3%29%5E2+=36+ ALIGN=MIDDLE  ALT=\"4%28y+%2B+1%29%5E2-+%28x+%2B+3%29%5E2+=36+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y+%2B+1%29%5E2%2F36+-+%28x+%2B+3%29%5E2%2F36=36%2F36+ ALIGN=MIDDLE  ALT=\"4%28y+%2B+1%29%5E2%2F36+-+%28x+%2B+3%29%5E2%2F36=36%2F36+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+%2B+1%29%5E2%2F9-+%28x+%2B+3%29%5E2%2F36=1+ ALIGN=MIDDLE  ALT=\"%28y+%2B+1%29%5E2%2F9-+%28x+%2B+3%29%5E2%2F36=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+%2B+1%29%5E2%2F3%5E2-+%28x+%2B+3%29%5E2%2F6%5E2=1+ ALIGN=MIDDLE  ALT=\"%28y+%2B+1%29%5E2%2F3%5E2-+%28x+%2B+3%29%5E2%2F6%5E2=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The standard form of an hyperbola with the transverse axis being vertical.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+y+-+k+%29%5E2%2Fa%5E2+-+%28+x+-+h+%29%5E2%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28+y+-+k+%29%5E2%2Fa%5E2+-+%28+x+-+h+%29%5E2%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The center of the hyperbola is at the point ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >) or  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "semimajor axis length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "semiminor axis length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6 ALIGN=MIDDLE  ALT=\"+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The foci are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > units from the center of the hyperbola and is calculated from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+9+%2B+36+=45 ALIGN=MIDDLE  ALT=\"c%5E2+=+9+%2B+36+=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt+%2845%29=sqrt+%289%2A5%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt+%2845%29=sqrt+%289%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3sqrt%285%29 ALIGN=MIDDLE  ALT=\"c=3sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The foci are therefore, ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2Bc ALIGN=MIDDLE  ALT=\"k%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) or ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k-c ALIGN=MIDDLE  ALT=\"k-c\"   DISABLED_style= \"max-width:90%; height:auto;\" > )\r<BR>\n" );
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document.write( "or  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1-3sqrt%285%29 ALIGN=MIDDLE  ALT=\"+-1-3sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2B3sqrt%285%29 ALIGN=MIDDLE  ALT=\"-1%2B3sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "=>(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-7.7 ALIGN=MIDDLE  ALT=\"+-7.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.7 ALIGN=MIDDLE  ALT=\"5.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "The vertices are a units from the center of the hyperbola, ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+%2Ba ALIGN=MIDDLE  ALT=\"k+%2Ba\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) and ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+-a ALIGN=MIDDLE  ALT=\"k+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( "or ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) and ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > )\r<BR>\n" );
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document.write( "asymptotes: <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x%2F2%2B1%2F2 ALIGN=MIDDLE  ALT=\"+y+=+x%2F2%2B1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%28-3%2C-1%2C.12%29%2Clocate%28-3%2C-1%2CC%28-3%2C-1%29%29%2C%0D%0Acircle%28-3%2C-4%2C.12%29%2Clocate%28-3%2C-4%2Cv%28-3%2C-4%29%29%2C%0D%0Acircle%28-3%2C2%2C.12%29%2Clocate%28-3%2C2%2Cv%28-3%2C2%29%29%2C%0D%0Acircle%28-3%2C-7.7%2C.12%29%2Clocate%28-3%2C-7.7%2CF%28-3%2C-7.7%29%29%2C%0D%0Acircle%28-3%2C5.7%2C.12%29%2Clocate%28-3%2C5.7%2CF%28-3%2C5.7%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2F2%2B1%2F2%2C-x%2F2-5%2F2%2C-sqrt%289%28%28x+%2B+3%29%5E2%2F36%2B1%29%29-1+%2Csqrt%289%28%28x+%2B+3%29%5E2%2F36%2B1%29%29-1%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
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