document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191271>Question 1191271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the circle having the points (2,10) and (-8,-14) the ends of its diameter. ​ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823077 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3820)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=823077\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Any circle has two defining properties:<BR>\n" );
document.write( "<ul><li>Center</li><li>Radius</li></ul>Let's first find the center. <BR>\n" );
document.write( "This is the same as finding the midpoint of those two endpoints on the diameter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Focus on the x coordinates for now.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add them up: 2+(-8) = -6<BR>\n" );
document.write( "Divide the result in half: -6/2 = -3<BR>\n" );
document.write( "This is the x coordinate of the midpoint.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Repeat those steps for the y coordinates:<BR>\n" );
document.write( "Add: 10+(-14) = -4<BR>\n" );
document.write( "Divide by two: -4/2 = -2<BR>\n" );
document.write( "This is the y coordinate of the midpoint.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The midpoint is located at (-3,-2)<BR>\n" );
document.write( "This is the center of the circle.<BR>\n" );
document.write( "Center = (h,k) = (-3,-2)<BR>\n" );
document.write( "Or to break it down further, we have h = -3 and k = -2 pair up together.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now to find the radius.<BR>\n" );
document.write( "The radius is the distance from the center to any point on the edge of the circle.<BR>\n" );
document.write( "I'll use the distance formula to calculate the distance from the endpoint (2,10) to the center (-3,-2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x1,y1) = (2,10) and (x2, y2) = (-3,-2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = \sqrt{(2-(-3))^2 + (10-(-2))^2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = \sqrt{(2+3)^2 + (10+2)^2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = \sqrt{(5)^2 + (12)^2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = \sqrt{25 + 144}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = \sqrt{169}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d = 13\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The distance from (2,10) to (-3,-2) is exactly 13 units.<BR>\n" );
document.write( "Therefore, the radius is r = 13.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To recap, we found:<BR>\n" );
document.write( "h = -3<BR>\n" );
document.write( "k = -2<BR>\n" );
document.write( "r = 13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The circle template <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > will update to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-3%29%29%5E2+%2B+%28y-%28-2%29%29%5E2+=+13%5E2 ALIGN=MIDDLE  ALT=\"%28x-%28-3%29%29%5E2+%2B+%28y-%28-2%29%29%5E2+=+13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > after plugging in those values mentioned. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplifying things gets us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2%2B%28y%2B2%29%5E2+=+169 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2B%28y%2B2%29%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/GeZ9WQN.png\"><BR>\n" );
document.write( "The diagram was made using GeoGebra.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2%2B%28y%2B2%29%5E2+=+169 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2B%28y%2B2%29%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Center = (-3,-2) and radius = 13<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );