document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=867576>Question 867576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the ellipse with foci (2,-4) and (2,8) and with a   vertex at (2,10) . Hint:A vertex is located at one end of the major axis </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #523100 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=523100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the ellipse with foci (2,-4) and (2,8) and with a vertex at (2,10) . <BR>\n" );
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document.write( "Given data shows ellipse has a vertical major axis. (y-coordinates of foci change but x-coordinates do not)<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=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a>b, (h,k)=coordinates of center<BR>\n" );
document.write( "For given ellipse:<BR>\n" );
document.write( "y-coordinate of center=2(midpoint between -4 and 8)<BR>\n" );
document.write( "x-coordinate of center=2<BR>\n" );
document.write( "center:(2,2)<BR>\n" );
document.write( "a=8 (distance from center to vertex on the vertical major axis)<BR>\n" );
document.write( "a^2=64<BR>\n" );
document.write( "c=6  (distance from center to foci on the vertical major axis)<BR>\n" );
document.write( "c^2=36<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=64-36=28<BR>\n" );
document.write( "Equation:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2F28%2B%28y-2%29%5E2%2F64=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2F28%2B%28y-2%29%5E2%2F64=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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