document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=428941>Question 428941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the Ellipse, in Standard Form:  Foci:  (-1, -2), (-1, 6) Vertices:  (-1, -6), (-1, 10) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #298723 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=298723\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the Ellipse, in Standard Form: Foci: (-1, -2), (-1, 6) Vertices: (-1, -6), (-1, 10)<BR>\n" );
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document.write( "Standard form of ellipse for horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b)<BR>\n" );
document.write( "Standard form of ellipse for vertical major axis: (y-k)^2/a^2+(x-h)^2/b^2=1 (a>b)<BR>\n" );
document.write( "In both forms, (h,k) represent the (x,y) coordinates of the center.<BR>\n" );
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document.write( "Given data shows this ellipse has a vertical major axis on line x=-1, so, it is of the second form:<BR>\n" );
document.write( "Center:(-1,2) (half way between foci or vertices on the major axis)<BR>\n" );
document.write( "Length of major axis=16 (between vertices on the major axis)=2a<BR>\n" );
document.write( "2a=16<BR>\n" );
document.write( "a=8<BR>\n" );
document.write( "a^2=64<BR>\n" );
document.write( "c=4(from ctr to either foci on major axis)<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=64-16=48<BR>\n" );
document.write( "b=sqrt(48)<BR>\n" );
document.write( "b^2=48<BR>\n" );
document.write( "We now have the information we need to write the equation of this ellipse:\r<BR>\n" );
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document.write( "(y-2)^2/64+(x+1)^2/48=1\r<BR>\n" );
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document.write( "see the graph below as a visual check on the answers above\r<BR>\n" );
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document.write( "..<BR>\n" );
document.write( "y=(64(1-(x+1)^2/48))^.5+2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-12%2C12%2C+-12%2C+12%2C+%2864%281-%28x%2B1%29%5E2%2F48%29%29%5E.5%2B2%2C-%2864%281-%28x%2B1%29%5E2%2F48%29%29%5E.5%2B2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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