document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=583783>Question 583783</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I write the standard equation for the circle that passes through the points: <BR>\n" );
document.write( "(-1, 2) <BR>\n" );
document.write( "(4, 2) <BR>\n" );
document.write( "(- 3, 4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372606 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=372606\">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( "Use the idea that the perpendicular bisector of any chord of a circle passes through the center of the circle.  Since the given points are on the circle, any pair of the three points are the endpoints of a line segment that is a chord of the circle.\r<BR>\n" );
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document.write( "Select 2 of the three given points.\r<BR>\n" );
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document.write( "Step 1:  Calculate the midpoint of the segment connecting those two points using the midpoint formulas:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_m\ = \frac{x_1 + x_2}{2}\"> and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y_m\ = \frac{y_1 + y_2}{2}\">\r<BR>\n" );
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document.write( "Step 2:  Calculate the slope of the line containing the two selected points using the slope formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{y_1\ -\ y_2}{x_1\ -\ x_2} \">\r<BR>\n" );
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document.write( "Step 3:  Determine the slope of the perpendicular to the segment.  Take the negative reciprocal of the slope calculated in step 2.\r<BR>\n" );
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document.write( "Step 4:  Derive an equation of the perpendicular bisector of the selected segment by using the point-slope form of an equation, the slope from step 3, and the midpoint from 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(x\ -\ x_1) \">\r<BR>\n" );
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document.write( "Choose a different pair of points and repeat the process.\r<BR>\n" );
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document.write( "Take the two equations of the perpendicular bisectors as a 2X2 system and solve for the point of intersection, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (h,\,k)\"> which is the center of the circle.\r<BR>\n" );
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document.write( "Use a modified form of the distance formula to calculate the radius squared:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ r^2\ =\ (x_1\ -\ h)^2\ +\ (y_1\ -\ k)^2\">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x_1,y_1)\"> is any of the initially given points.\r<BR>\n" );
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document.write( "Using the coordinates of the center and the radius, write the standard form equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ h)^\ +\ (y\ -\ k)^2\ =\ r^2\">\r<BR>\n" );
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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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