document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=955294>Question 955294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the ellipse with a vertex at (4,10), and foci at (4,2) and (4,8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #583685 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=583685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The foci allow finding the center, and then that one given vertex lets you know value for variable a.\r<BR>\n" );
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document.write( "CENTER:  On line x=4, y value is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B8%29%2F2=5 ALIGN=MIDDLE  ALT=\"%282%2B8%29%2F2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Note that foci are in a vertical arrangement so \"a\" goes under the y-rational expression.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=10-5=5 ALIGN=MIDDLE  ALT=\"a=10-5=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Currently we have a=5 and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28%28x-4%29%5E2%2Fb%5E2%2B%28y-5%29%5E2%2F%285%5E2%29=1%29 ALIGN=MIDDLE  ALT=\"highlight_green%28%28x-4%29%5E2%2Fb%5E2%2B%28y-5%29%5E2%2F%285%5E2%29=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=b%5E2%2Bc%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=b%5E2%2Bc%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, from the graph and derivation of an ellipse with vertical axis of symmetry or either horizontal axis of symmetry.<BR>\n" );
document.write( "How far is center from either focus?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=c ALIGN=MIDDLE  ALT=\"3=c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "What was a?   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Find b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=a%5E2-c%5E2 ALIGN=MIDDLE  ALT=\"b%5E2=a%5E2-c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=25-9 ALIGN=MIDDLE  ALT=\"b%5E2=25-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=16 ALIGN=MIDDLE  ALT=\"b%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finish the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-4%29%5E2%2F4%5E2%2B%28y-5%29%5E2%2F%285%5E2%29=1%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-4%29%5E2%2F4%5E2%2B%28y-5%29%5E2%2F%285%5E2%29=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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