document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=950791>Question 950791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the point that is equidistant from (2,6) (-3,1) (8,-6). And I request that you use only formulas instead of drawing graphs. Thank you :)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580623 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=580623\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that this point (a,b) is the center of a circle and the points lie on the circle. <BR>\n" );
document.write( "The circle has equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bfx%2By%5E2%2Bgy%2Bh=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bfx%2By%5E2%2Bgy%2Bh=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Input each point,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B2f%2B36%2B6g%2Bh=0 ALIGN=MIDDLE  ALT=\"4%2B2f%2B36%2B6g%2Bh=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2f%2B6g%2Bh=-40 ALIGN=MIDDLE  ALT=\"2f%2B6g%2Bh=-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-3f%2B1%2Bg%2Bh=0 ALIGN=MIDDLE  ALT=\"9-3f%2B1%2Bg%2Bh=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3f%2Bg%2Bh=-10 ALIGN=MIDDLE  ALT=\"-3f%2Bg%2Bh=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2B8f%2B36-6g%2Bh=0 ALIGN=MIDDLE  ALT=\"64%2B8f%2B36-6g%2Bh=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8f-6g%2Bh=-100 ALIGN=MIDDLE  ALT=\"8f-6g%2Bh=-100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now subtract eq. 1 from eq. 2 to eliminate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3f%2Bg%2Bh-2f-6g-h=-10%2B40 ALIGN=MIDDLE  ALT=\"-3f%2Bg%2Bh-2f-6g-h=-10%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5f-5g=30 ALIGN=MIDDLE  ALT=\"-5f-5g=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2Bg=-6 ALIGN=MIDDLE  ALT=\"f%2Bg=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8f-6g%2Bh-2f-6g-h=-100%2B40 ALIGN=MIDDLE  ALT=\"8f-6g%2Bh-2f-6g-h=-100%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6f-12g=-60 ALIGN=MIDDLE  ALT=\"6f-12g=-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f-2g=-10 ALIGN=MIDDLE  ALT=\"f-2g=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract eq. 4 from eq. 5,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f-2g-f-g=-10-%28-6%29 ALIGN=MIDDLE  ALT=\"f-2g-f-g=-10-%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3g=-4 ALIGN=MIDDLE  ALT=\"-3g=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=4%2F3 ALIGN=MIDDLE  ALT=\"g=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2B4%2F3=-6 ALIGN=MIDDLE  ALT=\"f%2B4%2F3=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=-18%2F3-4%2F3 ALIGN=MIDDLE  ALT=\"f=-18%2F3-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=-22%2F3 ALIGN=MIDDLE  ALT=\"f=-22%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and finally,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3f%2Bg%2Bh=-10 ALIGN=MIDDLE  ALT=\"-3f%2Bg%2Bh=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2B4%2F3%2Bh=-10 ALIGN=MIDDLE  ALT=\"22%2B4%2F3%2Bh=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-30%2F3-4%2F3-66%2F3 ALIGN=MIDDLE  ALT=\"h=-30%2F3-4%2F3-66%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-100%2F3 ALIGN=MIDDLE  ALT=\"h=-100%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%2822%2F3%29x%2By%5E2%2B%284%2F3%29y-100%2F3=0 ALIGN=MIDDLE  ALT=\"x%5E2-%2822%2F3%29x%2By%5E2%2B%284%2F3%29y-100%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So now complete the square to find the center (h,k).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%2822%2F3%29x%2B%2811%2F3%29%5E2%2By%5E2%2B%284%2F3%29y%2B%282%2F3%29%5E2=100%2F3%2B%2811%2F3%29%5E2%2B%282%2F3%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-11%2F3%29%5E2%2B%28y%2B2%2F3%29%5E2=300%2F9%2B121%2F9%2B4%2F9 ALIGN=MIDDLE  ALT=\"%28x-11%2F3%29%5E2%2B%28y%2B2%2F3%29%5E2=300%2F9%2B121%2F9%2B4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-11%2F3%29%5E2%2B%28y%2B2%2F3%29%5E2=425%2F9 ALIGN=MIDDLE  ALT=\"%28x-11%2F3%29%5E2%2B%28y%2B2%2F3%29%5E2=425%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The center is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F3 ALIGN=MIDDLE  ALT=\"11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );