document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204888>Question 1204888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an archaeological site, a piece of a broken plate was dug up. It was put on top of a grid, with the arc of the plate passing through A (7, 2), B (1, 4) and C (−7, 0). Find its center and the standard equation of the circle describing the boundary of the plate. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841423 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the standard equation of the circle:\r<BR>\n" );
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document.write( "<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( "use point A (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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=%287-h%29%5E2%2B%282-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%287-h%29%5E2%2B%282-k%29%5E2=r%5E2\"   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=h%5E2+-+14h+%2B+k%5E2+-+4k+-+r%5E2+=+-53 ALIGN=MIDDLE  ALT=\"h%5E2+-+14h+%2B+k%5E2+-+4k+-+r%5E2+=+-53\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   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=r+=+sqrt%28h%5E2+-+14h+%2B+k%5E2+-+4k+%2B+53%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%28h%5E2+-+14h+%2B+k%5E2+-+4k+%2B+53%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.1\r<BR>\n" );
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document.write( "use point B (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=%281-h%29%5E2%2B%284-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%281-h%29%5E2%2B%284-k%29%5E2=r%5E2\"   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=h%5E2+-+2h+%2B+k%5E2+-+8k+-+r%5E2+=+-17 ALIGN=MIDDLE  ALT=\"h%5E2+-+2h+%2B+k%5E2+-+8k+-+r%5E2+=+-17\"   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=r+=+sqrt%28h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%28h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.2\r<BR>\n" );
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document.write( " and, use point  C (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0 ALIGN=MIDDLE  ALT=\"+0\"   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=%28-7-h%29%5E2%2B%280-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28-7-h%29%5E2%2B%280-k%29%5E2=r%5E2\"   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=h%5E2+%2B+14h+%2B+k%5E2+-+r%5E2+=+-49 ALIGN=MIDDLE  ALT=\"h%5E2+%2B+14h+%2B+k%5E2+-+r%5E2+=+-49\"   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=r+=+sqrt%28h%5E2+%2B+14h+%2B+k%5E2+%2B+49%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%28h%5E2+%2B+14h+%2B+k%5E2+%2B+49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.3\r<BR>\n" );
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document.write( "from eq.1 and eq.2 we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28h%5E2+-+14h+%2B+k%5E2+-+4k+%2B+53%29=sqrt%28h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17%29 ALIGN=MIDDLE  ALT=\"sqrt%28h%5E2+-+14h+%2B+k%5E2+-+4k+%2B+53%29=sqrt%28h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+14h+%2B+k%5E2+-+4k+%2B+53=h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17 ALIGN=MIDDLE  ALT=\"h%5E2+-+14h+%2B+k%5E2+-+4k+%2B+53=h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17\"   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=h%5E2+-+14h+%2B+k%5E2+-+4k+%2B+53-h%5E2+%2B2h+-+k%5E2+%2B+8k+-+17=0 ALIGN=MIDDLE  ALT=\"h%5E2+-+14h+%2B+k%5E2+-+4k+%2B+53-h%5E2+%2B2h+-+k%5E2+%2B+8k+-+17=0\"   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=-12h+%2B+4k+%2B+36+=+0 ALIGN=MIDDLE  ALT=\"-12h+%2B+4k+%2B+36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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=k+=+3h+-+9 ALIGN=MIDDLE  ALT=\"k+=+3h+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >......(1)\r<BR>\n" );
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document.write( "from eq.2 and eq.3 we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17%29=+sqrt%28h%5E2+%2B+14h+%2B+k%5E2+%2B+49%29 ALIGN=MIDDLE  ALT=\"sqrt%28h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17%29=+sqrt%28h%5E2+%2B+14h+%2B+k%5E2+%2B+49%29\"   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=h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17=+h%5E2+%2B+14h+%2B+k%5E2+%2B+49 ALIGN=MIDDLE  ALT=\"h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17=+h%5E2+%2B+14h+%2B+k%5E2+%2B+49\"   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=h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17-+h%5E2+-+14h+-+k%5E2+-+49=0 ALIGN=MIDDLE  ALT=\"h%5E2+-+2h+%2B+k%5E2+-+8k+%2B+17-+h%5E2+-+14h+-+k%5E2+-+49=0\"   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=-16h+-+8k+-+32+=+0 ALIGN=MIDDLE  ALT=\"-16h+-+8k+-+32+=+0\"   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=k+=+-2h+-+4 ALIGN=MIDDLE  ALT=\"k+=+-2h+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....(2)\r<BR>\n" );
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document.write( "from (1) and (2) we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3h+-+9=-2h+-+4 ALIGN=MIDDLE  ALT=\"3h+-+9=-2h+-+4\"   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=3h+%2B2h=9+-+4 ALIGN=MIDDLE  ALT=\"3h+%2B2h=9+-+4\"   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=5h=5 ALIGN=MIDDLE  ALT=\"5h=5\"   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=h=1 ALIGN=MIDDLE  ALT=\"h=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "go to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-2h+-+4 ALIGN=MIDDLE  ALT=\"k+=+-2h+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....(2), substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   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=k+=+-2+%2A1+-+4 ALIGN=MIDDLE  ALT=\"k+=+-2+%2A1+-+4\"   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=k=-2-4 ALIGN=MIDDLE  ALT=\"k=-2-4\"   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=k=-6 ALIGN=MIDDLE  ALT=\"k=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> the center is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "go to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+sqrt%28h%5E2+%2B+14h+%2B+k%5E2+%2B+49%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%28h%5E2+%2B+14h+%2B+k%5E2+%2B+49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.3, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+ ALIGN=MIDDLE  ALT=\"h+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k ALIGN=MIDDLE  ALT=\"+k\"   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=r+=+sqrt%281%5E2+%2B+14%2A1+%2B+%28-6%29%5E2+%2B+49%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%281%5E2+%2B+14%2A1+%2B+%28-6%29%5E2+%2B+49%29\"   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=r+=+sqrt%28100%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%28100%29\"   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=r+=+10 ALIGN=MIDDLE  ALT=\"r+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "equation of your circle is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%29%5E2%2B%28y-%28-6%29%29%5E2=10%5E2 ALIGN=MIDDLE  ALT=\"x-1%29%5E2%2B%28y-%28-6%29%29%5E2=10%5E2\"   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=%28x-1%29%5E2%2B%28y%2B6%29%5E2=100 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2%2B%28y%2B6%29%5E2=100\"   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=+drawing%28+600%2C+600%2C+-15%2C+15%2C+-20%2C+15%2C%0D%0Acircle%287%2C2%2C.14%29%2C+locate%287%2C2%2CA%287%2C2%29%29%2C%0D%0Acircle%281%2C4%2C.14%29%2C+locate%281%2C4%2CB%281%2C4%29%29%2C%0D%0Acircle%28-7%2C0%2C.14%29%2C+locate%28-7%2C0.98%2CC%28-7%2C0%29%29%2C%0D%0Acircle%281%2C-6%2C.14%29%2C+locate%281%2C-6%2CO%281%2C-6%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-15%2C+15%2C+-20%2C+15%2C+-sqrt%28-x%5E2%2B2x%2B99%29-6%2C+sqrt%28-x%5E2%2B2x%2B99%29-6%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );