document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192952>Question 192952</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (4,5) and (6,1) are the endpoints of the diameter, write the equation of this circle. i dont know what formulas to use or how to actually solve this problem  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144805 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=144805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Step 1: Find the center of the circle\r<BR>\n" );
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document.write( "To find the center of the circle, you need to find the midpoint of the diameter with (4,5) and (6,1) as the endpoints. So simply average the corresponding coordinates to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bmid%5D=%284%2B6%29%2F2=10%2F2=5 ALIGN=MIDDLE  ALT=\"x%5Bmid%5D=%284%2B6%29%2F2=10%2F2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the x-coordinate of the center is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmid%5D=%281%2B5%29%2F2=6%2F2=3 ALIGN=MIDDLE  ALT=\"y%5Bmid%5D=%281%2B5%29%2F2=6%2F2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the y-coordinate of the center is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the center is (5,3). Since the center of \r<BR>\n" );
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document.write( "<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;\" > \r<BR>\n" );
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document.write( "is (h,k), this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=5 ALIGN=MIDDLE  ALT=\"h=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2: Finding the radius\r<BR>\n" );
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document.write( "To find the radius, we need to find length of the diameter. To find the diameter's length, we need to find the distance from (4,5) to (6,1). To do that, we can use the distance formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: The point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_1,y_1\right)\"> is (4,5) which means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=4 ALIGN=MIDDLE  ALT=\"x%5B1%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=5 ALIGN=MIDDLE  ALT=\"y%5B1%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Similarly, the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_1,y_1\right)\"> is (6,1) which means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=6 ALIGN=MIDDLE  ALT=\"x%5B2%5D=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=1 ALIGN=MIDDLE  ALT=\"y%5B2%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the distance formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%284-6%29%5E2%2B%285-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%284-6%29%5E2%2B%285-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=4 ALIGN=MIDDLE  ALT=\"x%5B1%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=6 ALIGN=MIDDLE  ALT=\"x%5B2%5D=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=5 ALIGN=MIDDLE  ALT=\"y%5B1%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=1 ALIGN=MIDDLE  ALT=\"y%5B2%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28-2%29%5E2%2B%285-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28-2%29%5E2%2B%285-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28-2%29%5E2%2B%284%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28-2%29%5E2%2B%284%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%284%2B%284%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%284%2B%284%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%284%2B16%29 ALIGN=MIDDLE  ALT=\"d=sqrt%284%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"d=sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%284%2A5%29 ALIGN=MIDDLE  ALT=\"d=sqrt%284%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A5 ALIGN=MIDDLE  ALT=\"4%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%284%29%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"d=sqrt%284%29%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"d=2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the diameter is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long. Take half of this length to get the radius:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%282%2Asqrt%285%29%29%2F2=%28cross%282%29%2Asqrt%285%29%29%2Fcross%282%29=sqrt%285%29 ALIGN=MIDDLE  ALT=\"r=%282%2Asqrt%285%29%29%2F2=%28cross%282%29%2Asqrt%285%29%29%2Fcross%282%29=sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%285%29 ALIGN=MIDDLE  ALT=\"r=sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%285%29 ALIGN=MIDDLE  ALT=\"r=sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=%28sqrt%285%29%29%5E2=5 ALIGN=MIDDLE  ALT=\"r%5E2=%28sqrt%285%29%29%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=5 ALIGN=MIDDLE  ALT=\"r%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<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;\" > Start with the general formula for a circle\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2B%28y-3%29%5E2=5 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y-3%29%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=5 ALIGN=MIDDLE  ALT=\"h=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=5 ALIGN=MIDDLE  ALT=\"r%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the equation of the circle with the points (4,5) and (6,1) as the endpoints of the diameter is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2B%28y-3%29%5E2=5 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y-3%29%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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