document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=953474>Question 953474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the vertices of the hyperbola  x^2/9 - y^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 #582399 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=582399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 / 9 - y^2 / 4 = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the center is at (0,0)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is because the general equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-h)^2 / a^2 - (y-k)^2 / b^2 = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(h,k) is the center.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h = 0<BR>\n" );
document.write( "k = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(h,k) = (0,0)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That's the center of the hyperbola.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The vertices are at (-3,0) and (3,0).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that can be seen from the graph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "look below the graph for a further explanation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a graph of the equation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Csqrt%284%2A%28x%5E2%2F9-1%29%29%2C-sqrt%284%2A%28x%5E2%2F9-1%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a definition.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The hyperbola is centered on a point (h, k), which is the \"center\" of the hyperbola. The point on each branch closest to the center is that branch's \"vertex\". The vertices are some fixed distance a from the center. The line going from one vertex, through the center, and ending at the other vertex is called the \"transverse\" axis. The \"foci\" of an hyperbola are \"inside\" each branch, and each focus is located some fixed distance c from the center. (This means that a < c for hyperbolas.) The values of a and c will vary from one hyperbola to another, but they will be fixed values for any given hyperbola.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph is horizontally aligned because it's x^2 - y^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if it was y^2 - x^2, then the graph would be vertically aligned.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since a^2 is equal to 9, then a is equal to + or - 3 from the center of the hyperbola.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a link that explains the whole thing.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/hyperbola.htm\" target = \"_blank\">http://www.purplemath.com/modules/hyperbola.htm</>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );