document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206846>Question 206846</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Id have a question, did I understand/do this problem right?<BR>\n" );
document.write( "Problem; What is the equation of the ellipse with foci at (0,-4) and (0,4) and the sum of its focal radii being 10?<BR>\n" );
document.write( "My answer; 2a=10 a=5(sum of focal radii)<BR>\n" );
document.write( "(0+0/2, 4+4/2)= (0,4)<BR>\n" );
document.write( "c=4 b^2= a^2-c^2= 25-16=9<BR>\n" );
document.write( "equation of the ellipse is; <BR>\n" );
document.write( "(x-0)^2/25 + (y-4)^2/9=1<BR>\n" );
document.write( "(Is this right?)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156350 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=156350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Which definition does your book use?<BR>\n" );
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document.write( "This term has distinctly different definitions for different authors.\r<BR>\n" );
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document.write( "Usage 1: For some authors, this refers to the distance from the center to the focus for either an ellipse or a hyperbola. This definition of focal radius is usually written c.\r<BR>\n" );
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document.write( "Usage 2: For other authors, focal radius refers to the distance from a point on a conic section to a focus. In this case the focal radius varies depending where the point is on the curve (unless the conic in question is a circle). If there are two foci then there are two focal radii.\r<BR>\n" );
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document.write( "Note: Using this second definition, the sum of the focal radii of an ellipse is a constant. It is the same as the length of the major diameter. The difference of the focal radii of a hyperbola is a constant. It is the distance between the vertices.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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