document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888991>Question 888991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the standard form of the equation of the ellipse. vertices: (-4, -1), (-4, 11); endpoints of the minor axis: (-6, 5), (-2, 5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #538420 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=538420\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is as follows:\r<BR>\n" );
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document.write( "(x+4)^2/4 + (y-6)^2/36 = 1\r<BR>\n" );
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document.write( "the graph of your equation is shown below:\r<BR>\n" );
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document.write( "look below the graph for further comments.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/072806.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the length of your vertical axis is equal to (11 - (-1)) = 12.<BR>\n" );
document.write( "the length of your horizontal axis is equal to (-6 - (-2) = 4.\r<BR>\n" );
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document.write( "the general form of the equation of an ellipse is:\r<BR>\n" );
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document.write( "(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1\r<BR>\n" );
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document.write( "a is half the length of the horizontal axis which is equal to 2 which makes a^2 = 4.\r<BR>\n" );
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document.write( "b is half the length of the vertical axis which is equal to 6 which makes b^2 = 36\r<BR>\n" );
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document.write( "c is the distance between the focal points.\r<BR>\n" );
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document.write( "the formula for c is:\r<BR>\n" );
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document.write( "c^2 = |a^2 - b^2|\r<BR>\n" );
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document.write( "the absolute value sign is necessary because c is always positive and sometimes a is bigger than b (horizontal major axis) and sometimes b is bigger than a (vertical major axis.\r<BR>\n" );
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document.write( "your c^2 is equal to |4-25| which is equal to 21 which makes c equal to sqrt(21).\r<BR>\n" );
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document.write( "your focal points will be along the major axis at (-4,6-sqrt(21)) and (-4,6+sqrt(21)).\r<BR>\n" );
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document.write( "on the graph these focal points show up at (-4,0.417) and (-4,9.583).\r<BR>\n" );
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document.write( "the center of your graph is midway between the  vertices which puts it at (-4,5).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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