document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158612>Question 1158612</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation of the circle that passes through the 3 points (5, -7), (2, -4), and (5, -3). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781560 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=781560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( " the 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( "if the circle  passes through the 3 points (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we will use them to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <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=%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;\" > .....plug in coordinates of the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   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=%285-h%29%5E2%2B%28-7-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%285-h%29%5E2%2B%28-7-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=25-10h%2Bh%5E2%2B49%2B14k%2Bk%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"25-10h%2Bh%5E2%2B49%2B14k%2Bk%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%2Bk%5E2-10h%2B14k%2B49%2B25=r%5E2 ALIGN=MIDDLE  ALT=\"h%5E2%2Bk%5E2-10h%2B14k%2B49%2B25=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+10+h+%2B+k%5E2+%2B+14+k+%2B+74=r%5E2 ALIGN=MIDDLE  ALT=\"h%5E2+-+10+h+%2B+k%5E2+%2B+14+k+%2B+74=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.1\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;\" > .....plug in coordinates of the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-h%29%5E2%2B%28-4-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%282-h%29%5E2%2B%28-4-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+4+h+%2B+k%5E2+%2B+8+k+%2B+20=r%5E2 ALIGN=MIDDLE  ALT=\"h%5E2+-+4+h+%2B+k%5E2+%2B+8+k+%2B+20=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.2\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;\" > .....plug in coordinates of the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-h%29%5E2%2B%28-3-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%285-h%29%5E2%2B%28-3-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+10+h+%2B+k%5E2+%2B+6+k+%2B+34=r%5E2 ALIGN=MIDDLE  ALT=\"h%5E2+-+10+h+%2B+k%5E2+%2B+6+k+%2B+34=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.3\r<BR>\n" );
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document.write( "subtract eq.2 from eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+10+h+%2B+k%5E2+%2B+14+k+%2B+74-%28h%5E2+-+4+h+%2B+k%5E2+%2B+8+k+%2B+20%29=r%5E2-r%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ......simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+10+h+%2B+k%5E2+%2B+14+k+%2B+74-h%5E2+%2B4+h+-+k%5E2+-+8+k+-+20=0 ALIGN=MIDDLE  ALT=\"h%5E2+-+10+h+%2B+k%5E2+%2B+14+k+%2B+74-h%5E2+%2B4+h+-+k%5E2+-+8+k+-+20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6h%2B6k%2B54=0 ALIGN=MIDDLE  ALT=\"-6h%2B6k%2B54=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........simplify, both sides divide by <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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-h%2Bk%2B9=0 ALIGN=MIDDLE  ALT=\"-h%2Bk%2B9=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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=h-9 ALIGN=MIDDLE  ALT=\"k=h-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.1a\r<BR>\n" );
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document.write( "subtract eq.3 from eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+4+h+%2B+k%5E2+%2B+8+k+%2B+20-%28h%5E2+-+10+h+%2B+k%5E2+%2B+6+k+%2B+34%29=r%5E2-r%5E2 ALIGN=MIDDLE  ALT=\"h%5E2+-+4+h+%2B+k%5E2+%2B+8+k+%2B+20-%28h%5E2+-+10+h+%2B+k%5E2+%2B+6+k+%2B+34%29=r%5E2-r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >........simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+4+h+%2B+k%5E2+%2B+8+k+%2B+20-h%5E2+%2B+10+h+-+k%5E2+-+6+k+-+34=0 ALIGN=MIDDLE  ALT=\"h%5E2+-+4+h+%2B+k%5E2+%2B+8+k+%2B+20-h%5E2+%2B+10+h+-+k%5E2+-+6+k+-+34=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2k+%2B+6+h++-+14=0 ALIGN=MIDDLE  ALT=\"+2k+%2B+6+h++-+14=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+%2B+3+h++-+7=0 ALIGN=MIDDLE  ALT=\"+k+%2B+3+h++-+7=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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=7-3h ALIGN=MIDDLE  ALT=\"+k+=7-3h\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.2a\r<BR>\n" );
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document.write( "from eq.1a and eq.2a we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h-9=7-3h ALIGN=MIDDLE  ALT=\"h-9=7-3h\"   DISABLED_style= \"max-width:90%; height:auto;\" >......solve for <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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2B3h=7%2B9 ALIGN=MIDDLE  ALT=\"h%2B3h=7%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4h=16 ALIGN=MIDDLE  ALT=\"4h=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=4 ALIGN=MIDDLE  ALT=\"h=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\n" );
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+=7-3h ALIGN=MIDDLE  ALT=\"+k+=7-3h\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.2a, 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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=7-3%2A4 ALIGN=MIDDLE  ALT=\"+k+=7-3%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=7-12 ALIGN=MIDDLE  ALT=\"+k+=7-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=-5 ALIGN=MIDDLE  ALT=\"+k+=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the center is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "plug it in\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y-%28-5%29%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y-%28-5%29%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y%2B5%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y%2B5%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >........now use the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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;\" >) to calculate <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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-4%29%5E2%2B%28-4%2B5%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%282-4%29%5E2%2B%28-4%2B5%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%5E2%2B%281%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28-2%29%5E2%2B%281%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B1=r%5E2 ALIGN=MIDDLE  ALT=\"4%2B1=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=5 ALIGN=MIDDLE  ALT=\"r%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and, your equation is:  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y-%28-5%29%29%5E2=5 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y-%28-5%29%29%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y%2B5%29%5E2=5 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y%2B5%29%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%285%2C-7%2C.12%29%2Clocate%285%2C-7%2Cp%285%2C-7%29%29%2C%0D%0Acircle%282%2C-4%2C.12%29%2Clocate%282%2C-4%2Cp%282%2C-4%29%29%2C%0D%0Acircle%285%2C-3%2C.12%29%2Clocate%285%2C-3%2Cp%285%2C-3%29%29%2C%0D%0Acircle%284%2C-5%2C.12%29%2Clocate%284%2C-5%2CC%284%2C-5%29%29%2C%0D%0A%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C-sqrt%285-%28x-4%29%5E2%29-5+%2Csqrt%285-%28x-4%29%5E2%29-5%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );