document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139392>Question 139392</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0030700442/algebrahomeworkh>Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> What is the answer in standard form and the center and radius of this circle equation?<BR>\n" );
document.write( "3x^2+3y^2-18x+6y=18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101648 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=101648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You mean the 'equation' in standard form, I think.\r<BR>\n" );
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document.write( "The standard form of an equation of a circle with center at (h,k) and radius r is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice that the terms on the left are each a squared binomial, so the trick to converting an equation in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBy%5E2%2BCx%2BDy%2BC=0 ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBy%5E2%2BCx%2BDy%2BC=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > into standard form is to complete the square on each of the variables.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B3y%5E2-18x%2B6y=18 ALIGN=MIDDLE  ALT=\"3x%5E2%2B3y%5E2-18x%2B6y=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice that all of the coefficients on this one are divisible by 3, so divide through by 3 first because we need the coefficients on the 2nd degree terms to be 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-6x%2B2y=6 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-6x%2B2y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an equivalent equation and describes the same conic section.\r<BR>\n" );
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document.write( "Next rearrange the terms so that the x terms are together and the y terms are together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2By%5E2%2B2y=6 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2By%5E2%2B2y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide the coefficient on the 1st degree x term by 2, square the result, and add that result to both sides of the equation:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%2F2%29%5E2=%28-3%29%5E2=9 ALIGN=MIDDLE  ALT=\"%28-6%2F2%29%5E2=%28-3%29%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9%2By%5E2%2B2y=6%2B9 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9%2By%5E2%2B2y=6%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Do the same thing with the coefficient on the 1st degree y term:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F2%29%5E2=1%5E2=1 ALIGN=MIDDLE  ALT=\"%282%2F2%29%5E2=1%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and collect terms on the right\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9%2By%5E2%2B2y%2B1=6%2B9%2B1 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9%2By%5E2%2B2y%2B1=6%2B9%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9%2By%5E2%2B2y%2B1=16 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9%2By%5E2%2B2y%2B1=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have a sum of two perfect square trinomials:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9=%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9=%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B2y%2B1=%28y%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"y%5E2%2B2y%2B1=%28y%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2B%28y%2B1%29%5E2=16 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2B%28y%2B1%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=4%5E2 ALIGN=MIDDLE  ALT=\"16=4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2B%28y%2B1%29%5E2=4%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2B%28y%2B1%29%5E2=4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now compare this result to the standard form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  We need to make one little adjustment to make our result look exactly like the standard form pattern:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2B%28y-%28-1%29%29%5E2=4%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2B%28y-%28-1%29%29%5E2=4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we can read the coordinates of the center and the value of the radius directly.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-1 ALIGN=MIDDLE  ALT=\"k=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the center is at (3,-1)\r<BR>\n" );
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document.write( "and the radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4 ALIGN=MIDDLE  ALT=\"r=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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