document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=491838>Question 491838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graph the hyperbola and label the vertices, foci and asymptotes:<BR>\n" );
document.write( "(((y+2)^2)/25))-(((x+11)^2)/4)=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335375 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=335375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> graph the hyperbola and label the vertices, foci and asymptotes:<BR>\n" );
document.write( "(((y+2)^2)/25))-(((x+11)^2)/4)=1<BR>\n" );
document.write( "**<BR>\n" );
document.write( "graph the hyperbola and label the vertices, foci and asymptotes:<BR>\n" );
document.write( "((y+2)^2)/25)-((x+11)^2)/4)=1<BR>\n" );
document.write( "This is 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, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "From given data:<BR>\n" );
document.write( "Center: (-11,-2)<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)=(-11,-2±a)=(-11,-2±5)=(-11,3) and (-11,-7)<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=25+4=29<BR>\n" );
document.write( "c=&#8730;29=5.39<BR>\n" );
document.write( "Foci: (-11,-2±c)=(-11,-2±&#8730;29)=(-11,-2±5.39)=(-11,3.39) and (-11,-7.39)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes are straight lines thru the center with equation of the standard form: y=mx+b, with m=slope and b=y-intercept.<BR>\n" );
document.write( "slope of asymptotes=±a/b=5/2 and -5/2<BR>\n" );
document.write( "Equations of asymptotes:<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "using coordinates of center to find b<BR>\n" );
document.write( "-2=5/2*-11+b<BR>\n" );
document.write( "-2=-55/2+b<BR>\n" );
document.write( "-4=-55+2b<BR>\n" );
document.write( "2b=51<BR>\n" );
document.write( "b=51/2<BR>\n" );
document.write( "Equation: y=5x/2+51/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "-2=-5/2*-11+b<BR>\n" );
document.write( "-2=55/2+b<BR>\n" );
document.write( "-4=55+2b<BR>\n" );
document.write( "2b=-59<BR>\n" );
document.write( "b=-59/2<BR>\n" );
document.write( "Equation: y=-5x/2-59/2<BR>\n" );
document.write( "Ans:<BR>\n" );
document.write( "Vertices:(-11,3) and (-11,-7)<BR>\n" );
document.write( "Foci: (-11,3.39) and (-11,-7.39)<BR>\n" );
document.write( "Equations of asymptotes:y=5x/2+51/2 and y=-5x/2-59/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "see the graph below as a visual check on the answers above<BR>\n" );
document.write( "y=±(25+25(x+11)^2/4)^.5-2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-20%2C+5%2C+-10%2C+10%2C%2825%2B25%28x%2B11%29%5E2%2F4%29%5E.5-2%2C-%2825%2B25%28x%2B11%29%5E2%2F4%29%5E.5-2%2C5x%2F2%2B51%2F2%2C-5x%2F2-59%2F2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );