document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=553905>Question 553905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hyperbola has a vertices at(0,±4) and a foci at (0,±9). Write its equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #361111 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=361111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A hyperbola has a vertices at(0,±4) and a foci at (0,±9). Write its equation.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Given equation is that 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 equation:<BR>\n" );
document.write( "center: (0,0)<BR>\n" );
document.write( "length of vertices=8=2a<BR>\n" );
document.write( "a=4<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "..<BR>\n" );
document.write( "foci: c=9<BR>\n" );
document.write( "c^2=81<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2<BR>\n" );
document.write( "b^2=c^2-a^2=81-16=65<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of given hyperbola:<BR>\n" );
document.write( "y^2/16-x^2/65=1 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );