document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=451902>Question 451902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find equation for the ellipse that shares a vertex and focus with the parabola x^2 + y = 100 and has its other focus at the origin?\r<BR>\n" );
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document.write( "I know what the shape of the two figures together would look like, and i found that 2C is 100, since that is the distance between foci. From that I determined that 2b - c = 100.  What I don't get is how to find a and b.  Thanks very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #310708 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=310708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You say that the ellipse shares a vertex (the point (0, 100)) and a focus with the parabola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y+=+100 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2+%2B+100 ALIGN=MIDDLE  ALT=\"y+=+-x%5E2+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%281%2F4%29%2A%28y+-+100%29+=+-%28x-0%29%5E2 ALIGN=MIDDLE  ALT=\"4%2A%281%2F4%29%2A%28y+-+100%29+=+-%28x-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Hence for the parabola, the distance from the vertex to the focus is 1/4. Also, one focus of the ellipse must be (0, 399/4).  It was given that the other focus of the ellipse is (0,0) (the origin).  The center of the ellipse is then the point (0, 399/8).  So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+399%2F4+-+399%2F8+=+399%2F8 ALIGN=MIDDLE  ALT=\"c+=+399%2F4+-+399%2F8+=+399%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+100+-+399%2F8+=+401%2F8 ALIGN=MIDDLE  ALT=\"a+=+100+-+399%2F8+=+401%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+a%5E2+-+c%5E2+=+25 ALIGN=MIDDLE  ALT=\"b%5E2+=+a%5E2+-+c%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then the standard equation  is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%28401%2F8%29%5E2+%2B+%28y+-+399%2F8%29%5E2%2F25+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F%28401%2F8%29%5E2+%2B+%28y+-+399%2F8%29%5E2%2F25+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2864x%5E2%29%2F160801+%2B+%28y-399%2F8%29%5E2%2F25+=+1 ALIGN=MIDDLE  ALT=\"%2864x%5E2%29%2F160801+%2B+%28y-399%2F8%29%5E2%2F25+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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