document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=820174>Question 820174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP!!!   An ellipse has a center at (-4,6) and passes through (-4,9) and (2,6). Find the equation of the ellipse, the coordinates of the vertices and foci. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #493446 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=493446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An ellipse has a center at (-4,6) and passes through (-4,9) and (2,6). Find the equation of the ellipse, the coordinates of the vertices and foci.<BR>\n" );
document.write( "***<BR>\n" );
document.write( "Given coordinates show this is an ellipse with horizontal major axis.<BR>\n" );
document.write( "Its standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,a>b, (h,k)=(x,y) coordinates of center.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2%2Fa%5E2%2B%28y-6%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2Fa%5E2%2B%28y-6%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "plug in coordinates of one given point (-4,9) on the ellipse.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2B4%29%5E2%2Fa%5E2%2B%289-6%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28-4%2B4%29%5E2%2Fa%5E2%2B%289-6%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B%283%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"0%2B%283%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "b=3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "plug in coordinates of 2nd given point (2,6) on the ellipse.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B4%29%5E2%2Fa%5E2%2B%286-6%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%282%2B4%29%5E2%2Fa%5E2%2B%286-6%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B4%29%5E2%2Fa%5E2%2B0=1 ALIGN=MIDDLE  ALT=\"%282%2B4%29%5E2%2Fa%5E2%2B0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%29%5E2%2Fa%5E2%2B0=1 ALIGN=MIDDLE  ALT=\"%286%29%5E2%2Fa%5E2%2B0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a^2=36<BR>\n" );
document.write( "a=6<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equation of given ellipse:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2%2F36%2B%28y-6%29%5E2%2F9=1 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2F36%2B%28y-6%29%5E2%2F9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "vertices:(-4±a,6)=(4±6,6)=(-2,6) and (10,6)<BR>\n" );
document.write( "c^2=a^2-b^2=36-9=27<BR>\n" );
document.write( "c=&#8730;27&#8776;5.2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "foci:(-4±c,6)=(4±5.2,6)=(-1.2,6) and (9.2,6)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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