document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=792682>Question 792682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Under what conditions does the equation x^2 + y^2 + 2gx + 2fy +c = 0 represent a circle<BR>\n" );
document.write( "1.with center on<BR>\n" );
document.write( "a) x axis <BR>\n" );
document.write( "b) y axis <BR>\n" );
document.write( "c) x and y axis \r<BR>\n" );
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document.write( "Can you please help me out? Thanks so much in advance:)<BR>\n" );
document.write( "Can you also please show the steps it would really help me understand better:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #480113 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=480113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Mostly a conic-section concept and symbolism exercise.  First, you want to Complete-the-Square for the x and the y, and convert the equation to standard form.  You will obtain something a little complicated, but you can use the formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+%2B+2gx+%2B+2fy+%2Bc+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+%2B+2gx+%2B+2fy+%2Bc+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > as given.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2gx%2By%5E2%2B2fy%2Bc=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2gx%2By%5E2%2B2fy%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The missing square term for x and for y are, in that order, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282g%2F2%29%5E2=g%5E2 ALIGN=MIDDLE  ALT=\"%282g%2F2%29%5E2=g%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282f%2F2%29%5E2=f%5E2 ALIGN=MIDDLE  ALT=\"%282f%2F2%29%5E2=f%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This will allow you to factor.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B2gx%2Bg%5E2%29%2B%28y%5E2%2B2fy%2Bf%5E2%29%2Bc-g%5E2-f%5E2=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B2gx%2Bg%5E2%29%2B%28y%5E2%2B2fy%2Bf%5E2%29%2Bc-g%5E2-f%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x%2Bg%29%5E2%2B%28y%2Bf%29%5E2=g%5E2%2Bf%5E2-c%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x%2Bg%29%5E2%2B%28y%2Bf%29%5E2=g%5E2%2Bf%5E2-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "According to that standard form equation for a circle, the center is at (-g,-f) and the radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28g%5E2%2Bf%5E2-c%29 ALIGN=MIDDLE  ALT=\"sqrt%28g%5E2%2Bf%5E2-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You should now be able to work through to the necessary conclusions.   </SPAN>\n" );
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