document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199445>Question 1199445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle passes through the points (6,3), (6,-3) and (2,5).Find the centre,radius, and equation of the circle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833327 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A circle passes through the points A(6,3), B(6,-3) and C(2,5).  Find the centre, radius, and equation of the circle<BR>\n" );
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document.write( "Find the perpendicular bisectors of AB and AC.<BR>\n" );
document.write( "For AB, it's the x-axis.<BR>\n" );
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document.write( "For AC:<BR>\n" );
document.write( "Find the midpoint:<BR>\n" );
document.write( "x: (6+2)/2 = 4<BR>\n" );
document.write( "y: (3+5)/2 = 4<BR>\n" );
document.write( "(4,4) is the midpoint<BR>\n" );
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document.write( "The slope of AC is (5-3)/(2-6) = -1/2<BR>\n" );
document.write( "The slope of lines perpendicular to AC = 2<BR>\n" );
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document.write( "Thru (4,4) with m = 2 ---> y-4 = 2(x-4)<BR>\n" );
document.write( "y = 2x-4 is the equation of the perpendicular bisector to AC<BR>\n" );
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document.write( "The intersection of y = 2x-4 and the x-axis is the center of the circle.<BR>\n" );
document.write( "At the x-axis, y = 0<BR>\n" );
document.write( "0 = 2x-4 ---> x = 2<BR>\n" );
document.write( "The center is (2,0)<BR>\n" );
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document.write( "The radius is the distance between the center and any of the 3 given points.<BR>\n" );
document.write( "r^2 = diffy^2 + diffx^2<BR>\n" );
document.write( "r^2 = (3-0)^2 + (6-2)^2 = 25<BR>\n" );
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