document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=618494>Question 618494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the center, vertices, foci, and asymptotes of the hyperbola?\r<BR>\n" );
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document.write( "x^2-9y^2+36y-72=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388943 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=388943\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do you find the center, vertices, foci, and asymptotes of the hyperbola? <BR>\n" );
document.write( "x^2-9y^2+36y-72=0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "x^2-9(y^2-4y+4)=72-36<BR>\n" );
document.write( "x^2-9(y-2)^2=36<BR>\n" );
document.write( "x^2/36-(y-2)^2/4=1<BR>\n" );
document.write( "This is an equation of a hyperbola with horizontal transverse axis.<BR>\n" );
document.write( "Form of equation:(x-h)^2/a^2-(y-k)^2/b^2=1<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "center: (0,2)<BR>\n" );
document.write( "a^2=36<BR>\n" );
document.write( "a=&#8730;36=6<BR>\n" );
document.write( "vertices: (0±a,2)=(0±6,2)=(-6,2) and (6,2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=4<BR>\n" );
document.write( "b=&#8730;4=2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=36+4=40<BR>\n" );
document.write( "c=&#8730;40&#8776;6.3<BR>\n" );
document.write( "foci: (0±c,2)=(0±6.3,2)=(-6.3,2) and (6.3,2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "slopes of asymptotes with horizontal transverse axis=±b/a=2=±2/6=±1/3<BR>\n" );
document.write( "Asymptotes are straight lines that intersect at center. Equation: y=mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with negative slope.<BR>\n" );
document.write( "y=-x/3+b<BR>\n" );
document.write( "solving for b using coordinates of center(0,2)<BR>\n" );
document.write( "2=0+b<BR>\n" );
document.write( "b=2<BR>\n" );
document.write( "Equation: y=-x/3+2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with positive slope.<BR>\n" );
document.write( "y=x/3+b<BR>\n" );
document.write( "solving for b using coordinates of center(0,2)<BR>\n" );
document.write( "2=0+b<BR>\n" );
document.write( "b=2<BR>\n" );
document.write( "Equation: y=x/3+2\r<BR>\n" );
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document.write( " </SPAN>\n" );
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