document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=446589>Question 446589</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the \"equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #307561 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=307561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the \"equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0\"<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Standard forms of an ellipse: <BR>\n" );
document.write( "With horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1,with (h,k) as (x,y) coordinates of the center (a>b)<BR>\n" );
document.write( "With vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, with (h,k) as (x,y) coordinates of the center (a>b)<BR>\n" );
document.write( "Note that if a, the larger number, is under x^2, the ellipse will have a horizontal major axis.<BR>\n" );
document.write( "If the larger number, is under y^2, the ellipse will have a vertical major axis.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "The best way to start solving given problem to draw a sketch of the ellipse with the points given.<BR>\n" );
document.write( "You will notice right away that the major axis is vertical.<BR>\n" );
document.write( "Length of major axis=12=2a<BR>\n" );
document.write( "a=6<BR>\n" );
document.write( "a^2=36<BR>\n" );
document.write( "length of minor axis=8=2b<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "b^2=16<BR>\n" );
document.write( "The center is somewhere on the major axis which lies on the line x=1<BR>\n" );
document.write( "The center is also somewhere on the minor axis which lies on the line y=0 or the x-axis<BR>\n" );
document.write( "Where these two lines cross is the center at (1,0)<BR>\n" );
document.write( "Now, we have the information to write the equation of the given ellipse as follows:\r<BR>\n" );
document.write( "\n" );
document.write( "(x+1)^2/16+y^2/36=1<BR>\n" );
document.write( "see the graph below\r<BR>\n" );
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document.write( "..<BR>\n" );
document.write( "y=(36(1-((x-1)^2/16)))^.5<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+10%2C%2836%281-%28%28x-1%29%5E2%2F16%29%29%29%5E.5%2C-%2836%281-%28%28x-1%29%5E2%2F16%29%29%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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