document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169048>Question 1169048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this.Finding the equation of ellipse given the center (2,0),focus (2,6),eccentricity 2/3.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794130 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=794130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The center is half-way between the two foci and the foci lie on the major axis.  So if the center is at (2,0) and one focus is at (2,6), the other focus is at (2,-6) and the major axis is on the line <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 2\">, a vertical line.\r<BR>\n" );
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document.write( "The distance from the center to either focus is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c\">, the distance from the center to a vertex on the major axis is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\">, and the distance from the center to a vertex on the minor axis is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\">. The eccentricity is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e\">\r<BR>\n" );
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document.write( "These quantities are related thusly:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e\ =\ \frac{c}{a}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c^2\ =\ a^2\ -\ b^2\">.\r<BR>\n" );
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document.write( "Once you have used the given data to calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\">, use the formula for an ellipse centered at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (h,k)\"> where the major axis is on a vertical line to derive your desired equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{(x\,-\,h)^2}{b^2}\,+\,\frac{(y\,-\,k)^2}{a^2}\ =\ 1\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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