document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=386132>Question 386132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the equation \r<BR>\n" );
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document.write( "2x^2 + 2y^2 -16x + 4y - 38 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #273015 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=273015\">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 \ \ \ \ \ \ \ \ \ \ 2x^2\ +\ 2y^2\ -\ 16x\ +\ 4y\ -\ 38\ =\ 0\">\r<BR>\n" );
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document.write( "First, what is it?  2nd degree equation in two variables.  Has to be a conic section.\r<BR>\n" );
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document.write( "Has both <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y^2\"> terms -- NOT a parabola.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y^2\"> terms have the same sign -- NOT a hyperbola.\r<BR>\n" );
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document.write( "The coefficients on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y^2\"> terms are equal -- NOT an ellipse.\r<BR>\n" );
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document.write( "Has to be a circle.\r<BR>\n" );
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document.write( "Find the center and radius.  Complete the square on each of the two variables.\r<BR>\n" );
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document.write( "Move the constant term into the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2x^2\ +\ 2y^2\ -\ 16x\ +\ 4y\ =\ 38\">\r<BR>\n" );
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document.write( "Group same type variables:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2x^2\ -\ 16x\ +\ 2y^2\ +\ 4y\ =\ 38\">\r<BR>\n" );
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document.write( "Divide by the lead coefficient:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 8x\ +\ y^2\ +\ 2y\ =\ 19\">\r<BR>\n" );
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document.write( "Divide the coefficient on th 1st degree x term by 2, square the result, add that result 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\ -\ 8x\ +\ 16\ +\ y^2\ +\ 2y\ =\ 19\ +\ 16\">\r<BR>\n" );
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document.write( "Repeat for the coefficient on the 1st degree y term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x^2\ -\ 8x\ +\ 16\right)\ +\ \left(y^2\ +\ 2y\ +\ 1\right)\ =\ 19\ +\ 16\ +\ 1\">\r<BR>\n" );
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document.write( "Factor the two perfect square trinomials in the LHS and simplify the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x^2\ -\ 4\right)^2\ +\ \left(y^2\ +\ 1\right)^2\ =\ 36\">\r<BR>\n" );
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document.write( "Hence you have a circle centered at (4,-1) with radius 6.\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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