document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198055>Question 198055</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the conic section represented by the equation: y^2 + 2y + 1 = 6x - x^2. Write in standard form and draw the graph. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148526 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=148526\">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( "First, put it in general form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2 - 6x + y^2 + 2y = -1\">\r<BR>\n" );
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document.write( "You have both an x-squared term and a y-squared term, so you eliminate parabola as the conic type.\r<BR>\n" );
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document.write( "The signs on these terms are the same so you eliminate hyperbola.\r<BR>\n" );
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document.write( "The coefficients on the high-order terms are equal, so you eliminate ellipse.\r<BR>\n" );
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document.write( "This is a circle.\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 \ \ \ \ \ \ \ \ \ \ x^2 - 6x + y^2 + 2y = -1\">\r<BR>\n" );
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document.write( "-6 divided by 2 is -3, squared is 9 -- add 9 to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2 - 6x + 9 + y^2 + 2y = -1 + 9\">\r<BR>\n" );
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document.write( "Complete the square on y:\r<BR>\n" );
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document.write( "2 divided by 2 is 1, squared is 1 -- add 1 to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2 - 6x + 9 + y^2 + 2y + 1 = -1 + 9 + 1 = 9\">\r<BR>\n" );
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document.write( "Factor the two perfect squares:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x - 3)^2 + (y + 1)^2 = 9\">\r<BR>\n" );
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document.write( "Center at (3,-1), radius 3.  You can draw your own graph.\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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