document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972484>Question 972484</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertices and foci of the hyperbola. Draw the graph. <BR>\n" );
document.write( "y^2/25 - x^2/21=1\r<BR>\n" );
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document.write( "x^2/9 - y^2/16=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594884 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=594884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the vertices and foci of the hyperbola. Draw the graph. <BR>\n" );
document.write( "y^2/25 - x^2/21=1<BR>\n" );
document.write( "center: (0,0)<BR>\n" );
document.write( "a^2=25<BR>\n" );
document.write( "a=5<BR>\n" );
document.write( "vertices: (0, 0±a)= (0, 0±5)=(0,-5) and (0,5)<BR>\n" );
document.write( "b^2=21<BR>\n" );
document.write( "c^2=a^2+b^2=25+21=46<BR>\n" );
document.write( "c=&#8730;46&#8776;6.8<BR>\n" );
document.write( "foci: (0, 0±c)= (0, 0±6.8)=(0,-6.8) and (0,6.8)<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "y=(25x^2/21+25)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%2825x%5E2%2F21%2B25%29%5E.5%2C-%2825x%5E2%2F21%2B25%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "x^2/9 - y^2/16=1<BR>\n" );
document.write( "center: (0,0)<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=3<BR>\n" );
document.write( "vertices: (0±a, 0)= (0±3, 0)=(-3, 0) and (4, 0)<BR>\n" );
document.write( "b^2=16<BR>\n" );
document.write( "c^2=a^2+b^2=9+16=25<BR>\n" );
document.write( "c=5<BR>\n" );
document.write( "foci:(0±c, 0)= (0±5, 0)=(-5, 0) and (5, 0)<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "y=(16x^2/9-16)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%2816x%5E2%2F9-16%29%5E.5%2C-%2816x%5E2%2F9-16%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );