document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=960769>Question 960769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertices and the foci of the ellipse with the given equation. Then draw the graph. 25x^2+16y^2=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #587193 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=587193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the vertices and the foci of the ellipse with the given equation. Then draw the graph. 25x^2+16y^2=1<BR>\n" );
document.write( "***<BR>\n" );
document.write( "given ellipse has a vertical major axis<BR>\n" );
document.write( "Its standard form of equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2%2B1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For given ellipse:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%28x%5E2%29%2B16%28y%5E2%29=1 ALIGN=MIDDLE  ALT=\"25%28x%5E2%29%2B16%28y%5E2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2F%281%2F25%29%2B%28y%5E2%29%2F%281%2F16%29=1 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2F%281%2F25%29%2B%28y%5E2%29%2F%281%2F16%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "center: (0,0)<BR>\n" );
document.write( "a^2=1/16<BR>\n" );
document.write( "a=1/4<BR>\n" );
document.write( "b^2=1/25<BR>\n" );
document.write( "b=1/5<BR>\n" );
document.write( "vertices: (0,±a)=(0, 0±(1/4))=(0, -(1/4)) and (0, (1/4)<BR>\n" );
document.write( "c^2=a^2-b^2=1/16-1/25=25/400-16/400=9/400<BR>\n" );
document.write( "c=3/20<BR>\n" );
document.write( "foci:  (0,±c)=(0, 0±(3/20))=(0, -(3/20)) and (0, (3/20)<BR>\n" );
document.write( ".. <BR>\n" );
document.write( "y=.25(1-25x^2)^.5<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-.5%2C+.5%2C+-.5%2C+.5%2C.25%281-25x%5E2%29%5E.5%2C-.25%281-25x%5E2%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );