document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=244978>Question 244978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the circle   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-4x%2B10y%2B20=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-4x%2B10y%2B20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179103 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to graph this circle, you need to solve for y.\r<BR>\n" );
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document.write( "solving for y gets you:\r<BR>\n" );
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document.write( "y = +/- sqrt (-x^2+4x+5) - 5\r<BR>\n" );
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document.write( "graph looks like this:\r<BR>\n" );
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document.write( "the center of this circle looks like it might be (x,y) = (2,-5).\r<BR>\n" );
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document.write( "in order to know for sure, we have to transform the equation into the proper form.\r<BR>\n" );
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document.write( "the proper form is (x-h)^2 + (y-k)^2 = r^2\r<BR>\n" );
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document.write( "where (h,k) is the center of the circle.\r<BR>\n" );
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document.write( "the original equation is:\r<BR>\n" );
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document.write( "x^2+y^2-4x+10y+20=0\r<BR>\n" );
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document.write( "move the terms around until you have all the x's together and all the y's together.\r<BR>\n" );
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document.write( "move the constant term to the right side of the equation.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "(x^2 - 4x) + (y^2 + 10y) = -20\r<BR>\n" );
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document.write( "complete the squares for both of these to get:\r<BR>\n" );
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document.write( "(x-2)^2 + (y+5)^2 = -20 + 4 + 25\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "(x-2)^2 + (y+5)^2 = 9\r<BR>\n" );
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document.write( "The center of the circle is at (x,y) = (2,-5) and the radius of the circle is 3.\r<BR>\n" );
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document.write( "the graph confirms that.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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