document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=424765>Question 424765</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the conic section with the given characteristics. Ellipse. Vertices at (4,-9) and (4,7) and Foci at (4,-6) and (4,4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296541 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=296541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the conic section with the given characteristics. Ellipse. Vertices at (4,-9) and (4,7) and Foci at (4,-6) and (4,4)\r<BR>\n" );
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document.write( "Based on given data, this is an ellipse with vertical major axis on x=4.<BR>\n" );
document.write( "Standard form for this ellipse: (y-k)^2/a^2+(x-h)^2/b^2=1 (a>b)<BR>\n" );
document.write( "The x-coordinate of center=4<BR>\n" );
document.write( "The y-coordinate of center=7+(-9)/2=-2/2=-1<BR>\n" );
document.write( "Center,therefore, is at (4,-1)<BR>\n" );
document.write( "2a=length of major axis=16<BR>\n" );
document.write( "a=8<BR>\n" );
document.write( "a^2=64<BR>\n" );
document.write( "c=5=distance from center on major axis,(y=-1) to either of given foci points(4,-6) or (4,4)<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=64-25=39<BR>\n" );
document.write( "b=sqrt(39)=6.24..(1/2 minor axis)<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "(y+1)^2/64+(x-4)^2/39=1<BR>\n" );
document.write( "See the graph of the ellipse below:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=+-((64-64(x-4)^2/39)^.5)-1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-12%2C+12%2C+-12%2C+12%2C+%28%2864-64%28x-4%29%5E2%2F39%29%5E.5%29-1%2C-%28%2864-64%28x-4%29%5E2%2F39%29%5E.5%29-1%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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