document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=783437>Question 783437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the equation is: 2x^2+2y^2+4y=0 and I am supposed to find the center and the radius of the circle as well as the x and y intercepts but I am not sure how to find the center and radius. If you could help me find those I can find the x and y intercepts. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #476783 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=476783\">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( "The equation of a circle with center at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x,\,k\right)\"> and radius <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x\ -\ h\right)^2\ +\ \left(y\ -\ k\right)^2\ =\ r^2\">.  So to address your situation, you need to make <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x^2\ +\ 2y^2\ +\ 4y\ =\ 0\"> look like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x\ -\ h\right)^2\ +\ \left(y\ -\ k\right)^2\ =\ r^2\">.  Actually, much easier than it looks.\r<BR>\n" );
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document.write( "The process requires you to complete the square on each of the two variables.  For this particular problem, dealing with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> is trivial since there is no first degree <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> term.  We know from that fact that the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\">, the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the center of the circle, is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0\">.\r<BR>\n" );
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document.write( "The first step in the process is to divide by the lead coefficient -- the one on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\"> term.  Of course, if this is to be a circle, the coefficient on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y^2\"> term has to be the same.  So you end up with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2\ +\ y^2\ +\ 2y\ =\ 0\">\r<BR>\n" );
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document.write( "Next, divide the coefficient on the 1st degree <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> term by 2 and square the result.  Add that result to both sides of the equation.  2 divided by 2 is 1. 1 squared is 1, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2\ +\ y^2\ +\ 2y\ +\ 1\ =\ 1\">\r<BR>\n" );
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document.write( "Now the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> term is a perfect square and the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> terms and the constant in the LHS form a perfect square, so factor:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2\ +\ \left(y\ +\ 1\right)^2\ =\ 1\">\r<BR>\n" );
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document.write( "Next, re-write everything so that it fits the circle equation pattern:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x\ -\ 0\right)^2\ +\ \left(y\ -\ (-1)\right)^2\ =\ 1^2\">\r<BR>\n" );
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document.write( "Now you can determine the center and radius by inspection:\r<BR>\n" );
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document.write( "Center:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,\,-1\right)\">\r<BR>\n" );
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document.write( "Radius:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 1\">\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( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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