document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144229>Question 1144229</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the standard form of the equation of the ellipse with center at (-4,7), a focus at (-4,11), and a vertex at (-4,12). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765260 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=765260\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%2847600%2F169%2C400%2C-10%2C1.9%2C-1.9%2C15%2C%0D%0Ared%28arc%28-4%2C7%2C6%2C10%29%29%2C%0D%0Agraph%2847600%2F169%2C400%2C-10%2C1.9%2C-1.9%2C15%29%2C%0D%0Acircle%28-4%2C7%2C.1%29%2C+circle%28-4%2C11%2C.1%29%2C+circle%28-4%2C12%2C.1%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "That is an ellipse with a vertical major axis, so it looks like the<BR>\n" );
document.write( "number zero 0, and has this standard equation:\r<BR>\n" );
document.write( "\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "where<BR>\n" );
document.write( "(h,k) = center = (-4,7)<BR>\n" );
document.write( "    a = distance from center to vertex = 5 units<BR>\n" );
document.write( "    c = distance from center to focus = 4 units.<BR>\n" );
document.write( "    b = distance from center to covertex, found by c²=a²-b²<BR>\n" );
document.write( "                                                   4²=5²-b²<BR>\n" );
document.write( "                                                   16=25-b²<BR>\n" );
document.write( "                                                   b²=25-16<BR>\n" );
document.write( "                                                   b²=9<BR>\n" );
document.write( "                                                    b=3<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-4%29%29%5E2%2F3%5E2%2B%28y-%287%29%29%5E2%2F4%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-%28-4%29%29%5E2%2F3%5E2%2B%28y-%287%29%29%5E2%2F4%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2%2F9%2B%28y-7%29%5E2%2F25=1 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2F9%2B%28y-7%29%5E2%2F25=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Edwin</pre> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );