document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=589451>Question 589451</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation for an ellipse that satisfies each set of conditions.<BR>\n" );
document.write( "endpoints of major axis at (3, -8) and (3, 4), foci at (3, -2+2 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+5+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) and (3, -2- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+5+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #374928 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=374928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation for an ellipse that satisfies each set of conditions.<BR>\n" );
document.write( "endpoints of major axis at (3, -8) and (3, 4), foci at (3, -2+2&#8730;5) and (3, -2-&#8730;5)<BR>\n" );
document.write( "**<BR>\n" );
document.write( "I will assume the 2nd given end point for the foci is (3,-2-2&#8730;5), not (3, -2-&#8730;5), as stated.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Standard form of equation for an ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k)=(x,y) coordinates of center.<BR>\n" );
document.write( "For given ellipse:<BR>\n" );
document.write( "x-coordinate of center=3<BR>\n" );
document.write( "y-coordinate of center=-2 (by midpoint formula)<BR>\n" );
document.write( "center: (3,-2)<BR>\n" );
document.write( "length of vertical major axis=12=2a (from -8 to 4)<BR>\n" );
document.write( "a=6<BR>\n" );
document.write( "a^2=36<BR>\n" );
document.write( "c=2&#8730;5 ( from foci)<BR>\n" );
document.write( "c^2=20<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=36-20=16<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "Equation of given ellipse:\r<BR>\n" );
document.write( "\n" );
document.write( "(x-3)^2/16+(y+2)^2/36=1<BR>\n" );
document.write( " </SPAN>\n" );
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