document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=448310>Question 448310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> endpoints of major axis at (2,12) and (2,-4, endpoints of minor axis at (4,4)(0,4) \r<BR>\n" );
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document.write( "How do you write the equation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308563 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=308563\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> endpoints of major axis at (2,12) and (2,-4, endpoints of minor axis at (4,4)(0,4) <BR>\n" );
document.write( "How do you write the equation?<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1 (a>b)<BR>\n" );
document.write( "Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b)<BR>\n" );
document.write( "Note that a^2 and b^2 have changed places in the two forms.<BR>\n" );
document.write( "This is an ellipse with a vertical major axis (First standard form listed above)<BR>\n" );
document.write( "x-coordinate of center=2<BR>\n" );
document.write( "y-coordinate of center=4<BR>\n" );
document.write( "center (2,4)<BR>\n" );
document.write( "Length of major axis=12+4=16=2a<BR>\n" );
document.write( "a=8<BR>\n" );
document.write( "a^2=64<BR>\n" );
document.write( "length of minor axis=4=2b<BR>\n" );
document.write( "b=2<BR>\n" );
document.write( "b^2=4<BR>\n" );
document.write( "c^2=a^2-b^2=64-4=60<BR>\n" );
document.write( "c=&#8730;60=7.75<BR>\n" );
document.write( "We now have enough information to write the equation of this elllipse<BR>\n" );
document.write( "(x-2)^2/4+(y-4)^2/64=1<BR>\n" );
document.write( "see the graph below as a visual check on the parameters above<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=((1-(x-2)^2/4)*64)^.5+4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+15%2C+%28%281-%28x-2%29%5E2%2F4%29%2A64%29%5E.5%2B4%2C-%28%281-%28x-2%29%5E2%2F4%29%2A64%29%5E.5%2B4%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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