document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=584566>Question 584566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this problem it the vertices are at 2,-9 and 2,7 and the foci are at 2,-11 and 2,9? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372836 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=372836\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> vertices are at 2,-9 and 2,7 and the foci are at 2,-11 and 2,9<BR>\n" );
document.write( "Given coordinates show 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<BR>\n" );
document.write( "using given coordinates of vertices:<BR>\n" );
document.write( "x-coordinate of center=2<BR>\n" );
document.write( "y-coordinate of center=(-9+7)/2=-1 (by midpoint formula)<BR>\n" );
document.write( "center: (2,-1)<BR>\n" );
document.write( "length of vertical transverse axis=-9 to 7=16=2a<BR>\n" );
document.write( "a=8<BR>\n" );
document.write( "a^2=64<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c=distance from center to one focus=-1 to 9=10<BR>\n" );
document.write( "c^2=100<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2<BR>\n" );
document.write( "b^2=c^2-a^2100-64=36<BR>\n" );
document.write( "b^2=36<BR>\n" );
document.write( "b=6<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "(y+1)^2/64-(x-2)^2/36=1<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );