document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=332784>Question 332784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the foci of the ellipse x^2/16+y^2/49=1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238471 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What are the foci of the ellipse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F16%2By%5E2%2F49=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F16%2By%5E2%2F49=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "==<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F16%2By%5E2%2F49=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F16%2By%5E2%2F49=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be rewritten as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4%5E2%2By%5E2%2F7%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4%5E2%2By%5E2%2F7%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "or in general<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for an ellipse with major axis along the x direction  (note:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%3Ea%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%3Ea%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for an ellipse with major axis along the y direction   (note:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%3Ea%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%3Ea%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "--<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4%5E2%2By%5E2%2F7%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4%5E2%2By%5E2%2F7%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "is an ellipse with the major axis along the y direction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=7%5E2+%3E+a%5E2=4%5E2 ALIGN=MIDDLE  ALT=\"b%5E2=7%5E2+%3E+a%5E2=4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the minor axis along the x direction<BR>\n" );
document.write( "centered at (h,k)=(0,0) \r<BR>\n" );
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document.write( "----<BR>\n" );
document.write( "In ellipses the focal length is 2*c, where c = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28b%5E2-a%5E2%29+=+sqrt%2849-16%29=5.745 ALIGN=MIDDLE  ALT=\"sqrt%28b%5E2-a%5E2%29+=+sqrt%2849-16%29=5.745\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so the foci for an ellipse with major axis along the y direction = (h,k-c), (h,k+c)<BR>\n" );
document.write( "since h=0, k=0, c=5.745, the foci are at (0,-5.745) and (0,5.745)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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