document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314735>Question 314735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me find the x and y intercepts of this circle: 9x^2 + 9x^2 -6x +12y -31=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225102 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=225102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9x^2\ +\ 9x^2\ -\ 6x\ +\ 12y\ -\ 31\ =\ 0\">\r<BR>\n" );
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document.write( "is most emphatically not a circle.  Can't be a circle without a y-squared term.  However, I suspect you made a little typo and really meant:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9x^2\ +\ 9y^2\ -\ 6x\ +\ 12y\ -\ 31\ =\ 0\">\r<BR>\n" );
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document.write( "Complete the square on x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9\left(x^2\ -\ \frac{2}{3}x\ +\ \frac{1}{9}\right)\ +\ 9y^2\ +\ 12y\ -\ 31\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9\left(x\ -\ \frac{1}{3}\right)^2\ +\ 9y^2\ +\ 12y\ -\ 31\ =\ 1\">\r<BR>\n" );
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document.write( "Complete the square on y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9\left(x\ -\ \frac{1}{3}\right)^2+\ 9\left(y^2\ +\ \frac{4}{3}y\ +\ \frac{4}{9}\right)\ -\ 31\ =\ 1\ +\ 4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9\left(x\ -\ \frac{1}{3}\right)^2+\ 9\left(y\  +\ \frac{2}{3}\right)^2\ -\ 31\ =\ 1\ +\ 4\">\r<BR>\n" );
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document.write( "And put the rest of the constant in the RHS\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9\left(x\ -\ \frac{1}{3}\right)^2+\ 9\left(y\  +\ \frac{2}{3}\right)^2\ =\ 36\">\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{9}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ -\ \frac{1}{3}\right)^2+\ \left(y\  +\ \frac{2}{3}\right)^2\ =\ 4\">\r<BR>\n" );
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document.write( "Circle, center at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(\frac{1}{3},-\frac{2}{3}\right)\"> and radius 2.\r<BR>\n" );
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document.write( "Substitute zero for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(0\ -\ \frac{1}{3}\right)^2+\ \left(y\  +\ \frac{2}{3}\right)^2\ =\ 4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(y\  +\ \frac{2}{3}\right)^2\ =\ \frac{35}{9}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(y\  +\ \frac{2}{3}\right)\ =\ \pm\frac{\sqrt{35}}{3}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -\frac{2}{3}\ \pm\ \frac{\sqrt{35}}{3}\">\r<BR>\n" );
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document.write( "Hence, the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> intercepts are:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(0,\frac{-2\ +\ \sqrt{35}}{3}\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(0,\frac{-2\ -\ \sqrt{35}}{3}\right)\">\r<BR>\n" );
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document.write( "Just substitute 0 for y in the circle equation and do the arithmetic as above to find the  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-intercepts.\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" );
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