document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119612>Question 1119612</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, these are five questions which I need help in<BR>\n" );
document.write( "Write the general equation for the circle that passes through the points:<BR>\n" );
document.write( "(1, 7)<BR>\n" );
document.write( "(8, 6)<BR>\n" );
document.write( "(7, -1) <BR>\n" );
document.write( "Write the general equation for the circle that passes through the points (1, 1), (1, 3), and (9, 2).<BR>\n" );
document.write( "Write the general equation for the circle that passes through the points (- 5, 0), (0, 4), and (2, 4).<BR>\n" );
document.write( "Write the general 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)<BR>\n" );
document.write( "Write the general equation for the circle that passes through the points:<BR>\n" );
document.write( "(0, 0)<BR>\n" );
document.write( "(6, 0)<BR>\n" );
document.write( "(0, - 8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735198 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=735198\">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( "Principles:\r<BR>\n" );
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document.write( "The perpendicular bisectors of any chords of a circle intersect in the center of the circle.\r<BR>\n" );
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document.write( "The slope of a perpendicular bisector is the negative reciprocal of the slope of the original line.\r<BR>\n" );
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document.write( "The distance from the center to any of the three given points is the radius.\r<BR>\n" );
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document.write( "Procedure:\r<BR>\n" );
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document.write( "Select any pair of the given points, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_1,y_1)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_2,y_2)\">, and use the slope formula to calculate the slope of the line containing those two points.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  m\ =\ \frac{y_2\ -\ y_1}{x_2\ -\ x_1}\">\r<BR>\n" );
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document.write( "Then calculate the negative reciprocal of this slope, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{1}{m}\">\r<BR>\n" );
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document.write( "Use the midpoint formulas to calculate the coordinates of the midpoint, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_m,\,y_m)\"> of the chord segment:\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}\">\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( "Derive the slope-intercept form of an equation of the line that has the negative reciprocal slope and passes through the calculated midpoint, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  y\ =\ -\frac{1}{m}(x\ -\ x_m)\ +\ y_m\">\r<BR>\n" );
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document.write( "Repeat the above process for a different pair of the given points.\r<BR>\n" );
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document.write( "Take the RHS of each of the derived equations and set them equal to each other.  Solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> to obtain the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the center of the desired circle.  Substitute this value and calculate the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-coordinate of the center of the circle.  You now have determined the circle center, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (h,\,k)\">\r<BR>\n" );
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document.write( "Use the distance formula with any one of the given points and the center, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (h,\,k)\"> to calculate the measure of the radius, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\">.  Since you will ultimately require only the square of the radius, you need not do the square root step in the distance formula.\r<BR>\n" );
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document.write( "Finally, construct the Standard Form:\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( "And then expand the binomials and collect like terms to create the General Form as required.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  x^2\ +\ y^2\ +\ Dx\ +\ Ey\ +\ F\ =\ 0\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large D\ =\ -2h,\ \ \"><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large E\ =\ -2k,\ \ \">and<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ F\ =\ h^2\ +\ k^2\ -\ r^2\"><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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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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