document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190993>Question 1190993</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of a circle that has a diameter with the endpoints given by the points A (2, -2) and B (-3, 3). </SPAN>\n" );
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document.write( "The x coordinates of points A and B are 2 and -3 respectively.<BR>\n" );
document.write( "Add up the x values: 2 + (-3) = -1<BR>\n" );
document.write( "Then cut that result in half: -1/2 = -0.5<BR>\n" );
document.write( "The x coordinate of the midpoint is x = -0.5\r<BR>\n" );
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document.write( "Repeat for the y coordinate of the midpoint.<BR>\n" );
document.write( "Add: -2+3 = 1<BR>\n" );
document.write( "Cut in half: 1/2 = 0.5<BR>\n" );
document.write( "The y coordinate of the midpoint is y = 0.5\r<BR>\n" );
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document.write( "The midpoint of segment AB is (-0.5, 0.5)<BR>\n" );
document.write( "This means (h,k) = (-0.5, 0.5) is the center of the circle, since AB is a diameter.<BR>\n" );
document.write( "In fraction form that would be (h,k) = (-1/2, 1/2)<BR>\n" );
document.write( "Let's label this point C. \r<BR>\n" );
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document.write( "To get the radius, find the distance from A to C.<BR>\n" );
document.write( "We'll use the aptly named distance formula.\r<BR>\n" );
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document.write( "A = (x1,y1) = (2,-2) and C = (x2, y2) = (-0.5, 0.5)\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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = \sqrt{(2-(-0.5))^2 + (-2-0.5)^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = \sqrt{(2+0.5)^2 + (-2-0.5)^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = \sqrt{(2.5)^2 + (-2.5)^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = \sqrt{6.25 + 6.25}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = \sqrt{12.5}\"><BR>\n" );
document.write( "The exact length of segment AC is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \sqrt{12.5}\">\r<BR>\n" );
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document.write( "This means the radius is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large r = \sqrt{12.5}\"><BR>\n" );
document.write( "Squaring both sides gets us <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large r^2 = 12.5\">\r<BR>\n" );
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document.write( "So we have<BR>\n" );
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/rendertex.cgi?\large (x-(-0.5))^2 + (y-0.5)^2 = 12.5\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large (x+0.5)^2 + (y-0.5)^2 = 12.5\"><BR>\n" );
document.write( "which is the equation of the circle.\r<BR>\n" );
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document.write( "Optionally you can replace each 0.5 with 1/2, and you can replace 12.5 with the improper fraction 25/2<BR>\n" );
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