document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=481667>Question 481667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the vertices, foci, and slope of the asymptotes for the hyperbola<BR>\n" );
document.write( "x^2/25 - y^2/36=1\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "Write the following equation in standard form and identify it as a parabola, ellipse, circle, or hyperbola:  4x^2+8x-9y^2-36y-68=0\r<BR>\n" );
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document.write( "thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329823 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=329823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Identify the vertices, foci, and slope of the asymptotes for the hyperbola<BR>\n" );
document.write( "x^2/25-y^2/36=1 <BR>\n" );
document.write( "and Write the following equation in standard form and identify it as a parabola, ellipse, circle, or hyperbola: 4x^2+8x-9y^2-36y-68=0 <BR>\n" );
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document.write( "x^2/25-y^2/36=1<BR>\n" );
document.write( "This is an equation of a hyperbola with horizontal transverse axis of the standard form with (h,k) being the center.<BR>\n" );
document.write( "(x-h)^2/a^2-(y-k)^2/b^2=1<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "Center:(0,0)<BR>\n" );
document.write( "a^2=25<BR>\n" );
document.write( "a=&#8730;25=5<BR>\n" );
document.write( "length of transverse axis=2a=10<BR>\n" );
document.write( "vertices (end-points of transverse axis)=0±a,0)=0±5,0)=(5,0) and (-5,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=36<BR>\n" );
document.write( "b=&#8730;36=6<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=25+36=61<BR>\n" );
document.write( "c=&#8730;61=7.8<BR>\n" );
document.write( "Foci: (0±c,0)=0±&#8730;61,0)=(&#8730;61,0) and (-&#8730;61,0)<BR>\n" );
document.write( "slope of asymptotes: ±b/a=±6/5<BR>\n" );
document.write( "...<BR>\n" );
document.write( "4x^2+8x-9y^2-36y-68=0<BR>\n" );
document.write( "4(x^2+2x+1)-9(y^2+4y+4)=68+4-36=36<BR>\n" );
document.write( "4(x+1)^2-9(y+2)^2=36<BR>\n" );
document.write( "Divide both sides by 36<BR>\n" );
document.write( "(x+1)^/9-(y+2)^2/4=1<BR>\n" );
document.write( "This is an equation of a hyperbola with horizontal transverse axis of the standard form: <BR>\n" );
document.write( "(x-h)^2/a^2-(y-k)^2/b^2=1 </SPAN>\n" );
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