document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=920729>Question 920729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i find the equation of an ellipse with the vertex at (0,-10) and the co-vertex at (6,0)? The center is (0,0). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558549 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=558549\">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=x%5E2%2By%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2FR%5E2%2By%5E2%2FR%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2FR%5E2%2By%5E2%2FR%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the equation of a circle of radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > centered at (0,0).<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%3C=x%5E2%2By%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%3C=x%5E2%2By%5E2=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%3C=R%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%3C=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-R%3C=x%3C=R ALIGN=MIDDLE  ALT=\"-R%3C=x%3C=R\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Similarly, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%3C=x%5E2%2By%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"y%5E2%3C=x%5E2%2By%5E2=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%3C=R%5E2 ALIGN=MIDDLE  ALT=\"y%5E2%3C=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-R%3C=y%3C=R ALIGN=MIDDLE  ALT=\"-R%3C=y%3C=R\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "An ellipse is just a circle stretched more in one direction than the other.<BR>\n" );
document.write( "In your case, you will have vertices at (0,-10) and (0,10),<BR>\n" );
document.write( "meaning that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10%3C=y%3C=10 ALIGN=MIDDLE  ALT=\"-10%3C=y%3C=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and co-vertices at (-6,0) and (6,0),<BR>\n" );
document.write( "meaning that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%3C=x%3C=6 ALIGN=MIDDLE  ALT=\"-6%3C=x%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "A circle with radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > would have the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F6%5E2%2By%5E2%2F6%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F6%5E2%2By%5E2%2F6%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and all its points would have to comply with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%3C=x%3C=6 ALIGN=MIDDLE  ALT=\"-6%3C=x%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%3C=y%3C=6 ALIGN=MIDDLE  ALT=\"-6%3C=y%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%3C=x%3C=6 ALIGN=MIDDLE  ALT=\"-6%3C=x%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the x coordinates,<BR>\n" );
document.write( "but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10%3C=y%3C=10 ALIGN=MIDDLE  ALT=\"-10%3C=y%3C=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the y coordinates,<BR>\n" );
document.write( "so the equation for the ellipse is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F6%5E2%2By%5E2%2F10%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F6%5E2%2By%5E2%2F10%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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