document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=634662>Question 634662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equations of the asymptotes.\r<BR>\n" );
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document.write( "y^2-9x^2-12y-36x-9=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #399804 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=399804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equations of the asymptotes. <BR>\n" );
document.write( "y^2-9x^2-12y-36x-9=0<BR>\n" );
document.write( "complete the squares<BR>\n" );
document.write( "y^2-12y-9x^2-36x-9=0<BR>\n" );
document.write( "(y^2-12y+36)-9(x^2+4x+4)=9+36-36<BR>\n" );
document.write( "(y-6)^2-9(x+2)^2=9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-6%29%5E2%2F9-%28x%2B2%29%5E2%2F1=1 ALIGN=MIDDLE  ALT=\"%28y-6%29%5E2%2F9-%28x%2B2%29%5E2%2F1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of a  hyperbola with vertical transverse axis:<BR>\n" );
document.write( "Its standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (h,k)=(x,y) coordinates of center<BR>\n" );
document.write( "..<BR>\n" );
document.write( "asymptotes are straight lines that intersect at the center.<BR>\n" );
document.write( "form of  equation: y=mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "slopes of asymptotes of hyperbolas with vertical transverse axis: ±a/b<BR>\n" );
document.write( "For given hyperbola: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-6%29%5E2%2F9-%28x%2B2%29%5E2%2F1=1 ALIGN=MIDDLE  ALT=\"%28y-6%29%5E2%2F9-%28x%2B2%29%5E2%2F1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "center: (-2,6)<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=3<BR>\n" );
document.write( "b^2=1<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "slope,m=±a/b=±3/1=±3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equation of asymptote with slope=-3<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "y=-3x+b<BR>\n" );
document.write( "solve for b using coordinates of center<BR>\n" );
document.write( "6=-3*-2+b<BR>\n" );
document.write( "b=0<BR>\n" );
document.write( "equation: y=-3x<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equation of asymptote with slope=3<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "y=3x+b<BR>\n" );
document.write( "solve for b using coordinates of center<BR>\n" );
document.write( "6=3*-2+b<BR>\n" );
document.write( "b=12<BR>\n" );
document.write( "equation: y=3x+12<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equations of asymptotes: y=-3x and y=3x+12<BR>\n" );
document.write( " </SPAN>\n" );
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