document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167474>Question 1167474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation for the circle that goes through the points (9,2) , (-1,12), and (-9,-4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792079 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Principle:  You need to find the center of the circle and the measure of the radius.  The perpendicular bisector of a chord of a circle passes through the center of the circle.  The distance from the center of the circle to any one of the given points is the desired radius.\r<BR>\n" );
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document.write( "1. Choose one pair of given points and calculate the midpoint of that line segment.\r<BR>\n" );
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document.write( "2. Calculate the slope of the line containing the line segment.\r<BR>\n" );
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document.write( "3. Calculate the negative reciprocal of the slope calculated in step 1.\r<BR>\n" );
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document.write( "4. Using the Point-Slope form of an equation of a line with the midpoint from step 2 and the slope from step 3, derive an equation for the perpendicular bisector of the line segment defined by the points chosen in step 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\m_{\text{perp}}(x\ -\ x_1)\">\r<BR>\n" );
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document.write( "5. Repeat steps 1 through 4 for a different pair of points.\r<BR>\n" );
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document.write( "6. Using the two equations from steps 4 and 5, solve the 2X2 system of linear equations to find the point of intersection of the two perpendicular bisectors of the two chosen chords.  This will be the center of the circle.\r<BR>\n" );
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document.write( "7. Using the distance formula, calculate the distance from the center to any one of the given points:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ \sqrt{ (x_1\,-\,x_2)^2\ +\ (y_1\,-\,y_2)^2}\">\r<BR>\n" );
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document.write( "Hint: Save yourself a little work.  Since you will need the radius squared in the formulation of the equation of the circle, you need not actually take the square root in the distance formula.\r<BR>\n" );
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document.write( "8. The equation of a circle centered at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (h,k)\"> with radius <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\,-\,h)^2\ +\ (y\,-\,k)^2\ =\ r^2\">\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solver91311&illustration_name=circle3points(2).jpg\">\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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