document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=558641>Question 558641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the polynomial equation with integer coefficients for the set of coplanar points described.\r<BR>\n" );
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document.write( "For each point,its distance from the fixed point (-3,0) is twice its distance from the fixed point (3,0)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363121 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=363121\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x,y\right)\"> be a point on the desired locus.\r<BR>\n" );
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document.write( "The distance from any point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x,y\right)\"> to the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-3,0\right)\"> is given by the distance formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d_1\ =\ \sqrt{(x\ -\ (-3))^2\ +\ (y\ -\ 0)^2}\ \ =\ \sqrt{(x\ +\ 3)^2\ +\ y^2}\">\r<BR>\n" );
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document.write( "Similarly, the distance from any point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x,y\right)\"> to the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(3,0\right)\"> is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d_2\ =\ \sqrt{(x\ -\ 3)^2\ +\ (y\ -\ 0)^2}\ \ =\ \sqrt{(x\ -\ 3)^2\ +\ y^2}\">\r<BR>\n" );
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document.write( "But we are also given that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d_1\ =\ 2d_2\"> so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{(x\ +\ 3)^2\ +\ y^2}\ =\ 2\sqrt{(x\ -\ 3)^2\ +\ y^2}\">\r<BR>\n" );
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document.write( "Square both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ +\ 3)^2\ +\ y^2\ =\ 4\left((x\ -\ 3)^2\ +\ y^2\right)\">\r<BR>\n" );
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document.write( "All you need to do is simplify, collect like terms, put everything of value on the left and a zero on the right and you are done.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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