document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30361>Question 30361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question:<BR>\n" );
document.write( "Find the center and radius of x^2+y^2-6x-2y-6=0\r<BR>\n" );
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document.write( "Possible Answers:<BR>\n" );
document.write( "(A) none of these<BR>\n" );
document.write( "(B) center (3,1) radius 16<BR>\n" );
document.write( "(C) center (3,1) radius 4<BR>\n" );
document.write( "(D) center (-3,-1) radius 16\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17075 by </B><A HREF=/tutors/aboutme.mpl?userid=Fermat><B>Fermat(136)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fermat><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=Fermat><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  x^2+y^2-6x-2y-6=0 \r<BR>\n" );
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document.write( "A circle, of radius r, and centred on the point (h,k) can be written as,<BR>\n" );
document.write( "(x-h)² + (y-k)² = r²<BR>\n" );
document.write( "expanding this expression,<BR>\n" );
document.write( "x² - 2hx + h² + y² - 2ky + k² = r²<BR>\n" );
document.write( "x² + y² - 2hx - 2ky + (h² + k² - r²) = 0<BR>\n" );
document.write( "comparing this with the expression we were given,<BR>\n" );
document.write( "x^2+y^2-6x-2y-6=0 <BR>\n" );
document.write( "and comparing coefficients,<BR>\n" );
document.write( "-2h = -6<BR>\n" );
document.write( "-2k = -2<BR>\n" );
document.write( "h² + k² - r² = -6<BR>\n" );
document.write( "From the 1st two eqns,<BR>\n" );
document.write( "h = 3<BR>\n" );
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document.write( "k = 1<BR>\n" );
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document.write( "substituting for h=3 and k=1 into the 3rd eqn,<BR>\n" );
document.write( "9 + 1 - r² = -6<BR>\n" );
document.write( "-r² = -16<BR>\n" );
document.write( "r² = 16<BR>\n" );
document.write( "r = 4<BR>\n" );
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document.write( "We therefore have: (h,k) = (3,1) and r = 4<BR>\n" );
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document.write( "Ans:C<BR>\n" );
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document.write( " </SPAN>\n" );
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