document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82853>Question 82853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle is defined by the following equation :\r<BR>\n" );
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document.write( "      3x^2+3y^2-24x+42y+183=0\r<BR>\n" );
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document.write( "  What is the radius? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59448 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=59448\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A circle is defined by the following equation :\r<BR>\n" );
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document.write( "      3x^2+3y^2-24x+42y+183=0\r<BR>\n" );
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document.write( "  What is the radius?<BR>\n" );
document.write( "The standard form of the equation of a circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where the center is (h,k) and the radius is r.<BR>\n" );
document.write( "First divide the whole equation by 3 because x^2 and y^2 have to have a coefficient of 1 in order to be in standard form.<BR>\n" );
document.write( "3x^2/3+3y^2/3-24x/3+42y/3+183/3=0/3<BR>\n" );
document.write( "x^2+y^2-8x+14y+61=0<BR>\n" );
document.write( "Group the x terms and y terms and subtract 61 from both sides of the equation<BR>\n" );
document.write( "x^2-8x+__+y^2+14y+___=-61+___+___<BR>\n" );
document.write( "We need to complete the square by taking half of the coefficients of x and y and squaring them and adding them to both sides of the equation.<BR>\n" );
document.write( "x^2-8x+(-8/2)^2+y^2+14y+(14/2)^2=-61+(-8/2)^2+(14/2)^2<BR>\n" );
document.write( "x^2-8x+(-4)^2+y^2+14y+(7)^2=-61+(-4)^2+(7)^2<BR>\n" );
document.write( "(x-4)^2+(y+7)^2=-61+16+49<BR>\n" );
document.write( "(x-4)^2+(y+7)^2=4<BR>\n" );
document.write( "(x-4)^2+(y+7)^2=2^2<BR>\n" );
document.write( "The radius is 2<BR>\n" );
document.write( "You didn't ask for the center, but it's (4,-7)<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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