document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581309>Question 581309</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Y^2-6y-4x^2-8x=95\r<BR>\n" );
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document.write( "Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola. 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 #371647 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=371647\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Y^2-6y-4x^2-8x=95 <BR>\n" );
document.write( "Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola. Then graph the hyperbola.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Y^2-6y-4x^2-8x=95<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "(y^2-6y+9)-4(x^2+2x+1)=95+9-4<BR>\n" );
document.write( "(y-3)^2-4(x+1)^2=100<BR>\n" );
document.write( "(y-3)^2/100-4(x+1)^2/25=1<BR>\n" );
document.write( "This is an equation of a hyperbola with vertical transverse axis of the standard form:<BR>\n" );
document.write( "(y-k)^2/a^2-(x-h)^2/b^2=1, (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "For given hyperbola:<BR>\n" );
document.write( "center: (-1,3)<BR>\n" );
document.write( "a^2=100<BR>\n" );
document.write( "a=10<BR>\n" );
document.write( "vertices=(-1,3±a)=(-1,3±10)=(-1,-7) and (-1,13)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=25<BR>\n" );
document.write( "b=5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=100+25=125<BR>\n" );
document.write( "c=&#8730;125&#8776;11.18<BR>\n" );
document.write( "Foci=(-1,3±c)=(-1,3±&#8730;125)=(-1,3±11.18)= (-1,-8.18) and (-1,14.18)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes:<BR>\n" );
document.write( "Asymptotes are straight lines which go thru the center and have slopes=±a/b<BR>\n" );
document.write( "slopes=10/5=2<BR>\n" );
document.write( "Standard form of equation for a straight line: y=mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "y=2x+b<BR>\n" );
document.write( "solving for b using coordinates of center<BR>\n" );
document.write( "3=2*-1+b<BR>\n" );
document.write( "b=5<BR>\n" );
document.write( "equation: y=2x+5 (asymptote with slope>0)<BR>\n" );
document.write( "y=-2x+b<BR>\n" );
document.write( "3=-2*-1+b<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "equation: y=-2x+1(asymptote with slope<0)<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "y=±(100+4(x+1)^2)^.5+3<BR>\n" );
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document.write( " </SPAN>\n" );
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