document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101761>Question 1101761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation an ellipse with foci (1,-1) and (1,-7) with major axis length 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716403 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13208)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=716403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The coordinates of the two foci are (1,-7) and (1,-1).  That tells us...<BR>\n" );
document.write( "(1) The center of the ellipse is (1,-4);<BR>\n" );
document.write( "(2) the major axis is vertical; and<BR>\n" );
document.write( "(3) the distance from the center to each focus is 3.<br><BR>\n" );
document.write( "The standard form for the equation of an ellipse with a vertical major axis is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-h%29%5E2%2Fb%5E2%29+%2B+%28%28y-k%29%5E2%2Fa%5E2%29+=+1 ALIGN=MIDDLE  ALT=\"%28%28x-h%29%5E2%2Fb%5E2%29+%2B+%28%28y-k%29%5E2%2Fa%5E2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(h,k) is the center of the ellipse ((1,-4) in this example);<BR>\n" );
document.write( "a is the semi-major axis (5 in this example);<BR>\n" );
document.write( "b is the semi-minor axis;<BR>\n" );
document.write( "and the values of a and b are related by the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where c is the distance from the center of the ellipse to each focus (3 in this example).<br><BR>\n" );
document.write( "In this example, since a is 5 and c is 3, b is 4.<br><BR>\n" );
document.write( "And now we have all the specific values needed to write the equation of this ellipse:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-1%29%5E2%2F4%5E2%29+%2B+%28%28y%2B4%29%5E2%2F5%5E2%29+=+1 ALIGN=MIDDLE  ALT=\"%28%28x-1%29%5E2%2F4%5E2%29+%2B+%28%28y%2B4%29%5E2%2F5%5E2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "or<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-1%29%5E2%2F16%29+%2B+%28%28y%2B4%29%5E2%2F25%29+=+1 ALIGN=MIDDLE  ALT=\"%28%28x-1%29%5E2%2F16%29+%2B+%28%28y%2B4%29%5E2%2F25%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );