document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866674>Question 866674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the circle that passes through the given points.<BR>\n" );
document.write( "(7,6),(11,6),(9,4)\r<BR>\n" );
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document.write( "answer:____________________________ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522424 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39799)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=522424\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using the standard form equation for a circle, you can make three separate equations for a system:\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%286-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%287-h%29%5E2%2B%286-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811-h%29%5E2%2B%286-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%2811-h%29%5E2%2B%286-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289-h%29%5E2%2B%284-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%289-h%29%5E2%2B%284-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Equating the left members of the first two equations, based on both equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that both members contain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286-k%29%5E2 ALIGN=MIDDLE  ALT=\"%286-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, allows you to find a value for h.\r<BR>\n" );
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document.write( "You can use this value for h to turn the variable expression in each of the three equations into a constant term; so now you will have three equations and just TWO unknowns, k and r.\r<BR>\n" );
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document.write( "I started this separately myself on paper, but not yet finished...<BR>\n" );
document.write( "This part just for h, but omitting to show the steps of the process:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28h=-2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28h=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...\r<BR>\n" );
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document.write( "Using that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-2 ALIGN=MIDDLE  ALT=\"h=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the equation Number 2 and Number 3 become:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169%2B%286-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"169%2B%286-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=121%2B%284-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"121%2B%284-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now equation each expression for both being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169%2B%286-k%29%5E2=121%2B%284-k%29%5E2 ALIGN=MIDDLE  ALT=\"169%2B%286-k%29%5E2=121%2B%284-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Performing the arithmetic, algebraic steps gives...<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28k=17%29 ALIGN=MIDDLE  ALT=\"highlight_green%28k=17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Use any of the original or transformed equations of the system to compute the value of r.  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2B%286-%28-17%29%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"81%2B%286-%28-17%29%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2B23%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"81%2B23%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=81%2B529 ALIGN=MIDDLE  ALT=\"r%5E2=81%2B529\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28r%5E2=610%29 ALIGN=MIDDLE  ALT=\"highlight_green%28r%5E2=610%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----see that this is still in the squared form.<BR>\n" );
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document.write( "The equation of the circle should be:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x%2B2%29%5E2%2B%28y-17%29%5E2=610%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x%2B2%29%5E2%2B%28y-17%29%5E2=610%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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