document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=627514>Question 627514</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the equation y²/25 - x²/16 . Then graph the hyperbola. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395397 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=395397\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the equation y²/25 - x²/16 . Then graph the hyperbola.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F25-x%5E2%2F16=1 ALIGN=MIDDLE  ALT=\"y%5E2%2F25-x%5E2%2F16=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of a hyperbola with vertical transverse axis.<BR>\n" );
document.write( "Its standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (h,k)=(x,y) coordinates of center.<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "center: (0,0)<BR>\n" );
document.write( "a^2=25<BR>\n" );
document.write( "a=&#8730;25=5<BR>\n" );
document.write( "Vertices: (0,0±a)+(0,0±5)=(0,-5) and (0,5)<BR>\n" );
document.write( "b^2=16<BR>\n" );
document.write( "b=&#8730;16=4<BR>\n" );
document.write( "c^2=a^2+b^2=25+16=41<BR>\n" );
document.write( "c=&#8730;41&#8776;6.4<BR>\n" );
document.write( "Foci:  (0,0±c)+(0,0±6.4)=(0,-6.4) and (0,6.4)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "slopes of asymptotes=±a/b=±5/4<BR>\n" );
document.write( "Equations of asymptotes:<BR>\n" );
document.write( "y=-5x/4<BR>\n" );
document.write( "and <BR>\n" );
document.write( "y=5x/4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "See graph below<BR>\n" );
document.write( "y=±(25+25x^2/16)^.5\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C10%2C+-10%2C+10%2C%2825%2B25x%5E2%2F16%29%5E.5%2C-%2825%2B25x%5E2%2F16%29%5E.5%2C-5x%2F4%2C5x%2F4%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );