document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471933>Question 471933</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the ellipse having the given points as foci and the given sum of the focal radii    \r<BR>\n" );
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document.write( "(-9, 0); (9, 0); 30 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323787 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=323787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the ellipse having the given points as foci and the given sum of the focal radii <BR>\n" );
document.write( "(-9, 0); (9, 0); 30<BR>\n" );
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document.write( "I could not fine anywhere the definition of \"focal radii\". I think you meant it to be the constant sum of the distances from any point of the ellipse to each focus. I will assume this is the intended definition which is equal to the major axis.<BR>\n" );
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document.write( "From given coordinates of the Foci, it can be seen that the equation has a horizontal major axis.(x changes but y does not) Standard form of ellipse for this equation: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center. <BR>\n" );
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document.write( "center: (0,0)<BR>\n" );
document.write( "major axis=2a=30<BR>\n" );
document.write( "a=15<BR>\n" );
document.write( "a^2=225<BR>\n" );
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document.write( "Also, from given coordinates of the Foci:<BR>\n" );
document.write( "c=9<BR>\n" );
document.write( "c^2=81=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=225-81=144<BR>\n" );
document.write( "b=12<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "x^2/225+y^2/144=1<BR>\n" );
document.write( "see graph below as a visual check on the answers\r<BR>\n" );
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document.write( "y=±(144-144x^2/225)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-20%2C+20%2C+-20%2C+20%2C%28144-144x%5E2%2F225%29%5E.5%2C-%28144-144x%5E2%2F225%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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