document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472993>Question 472993</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me find the general form of the equation of the circle<BR>\n" );
document.write( "With endpoints of a diameter at (-6,-2) and (-4,4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324319 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=324319\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Recall that the general equation of a circle is <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( "So we need the center (h,k) and the radius squared <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "First, let's find the center (h,k).\r<BR>\n" );
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document.write( "Since the center is the midpoint of the line segment with endpoints (-6,-2) and (-4,4), we need to find the midpoint.\r<BR>\n" );
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document.write( "X-Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D%2Bx%5B2%5D%29%2F2+=+%28-6%2B-4%29%2F2=-10%2F2+=+-5 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D%2Bx%5B2%5D%29%2F2+=+%28-6%2B-4%29%2F2=-10%2F2+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the x coordinate of midpoint is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 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;\" >\r<BR>\n" );
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document.write( "Y-Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5B1%5D%2By%5B2%5D%29%2F2+=+%28-2%2B4%29%2F2=2%2F2+=+1 ALIGN=MIDDLE  ALT=\"%28y%5B1%5D%2By%5B2%5D%29%2F2+=+%28-2%2B4%29%2F2=2%2F2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the y coordinate of midpoint is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=1 ALIGN=MIDDLE  ALT=\"k=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the center is the point (-5, 1)\r<BR>\n" );
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document.write( "Now let's find the radius squared\r<BR>\n" );
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document.write( "Use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=%28x-h%29%5E2%2B%28y-k%29%5E2 ALIGN=MIDDLE  ALT=\"r%5E2=%28x-h%29%5E2%2B%28y-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where (h,k) is the center and (x,y) is an arbitrary point on the circle.\r<BR>\n" );
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document.write( "In this case, <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=1 ALIGN=MIDDLE  ALT=\"k=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (drawn from one of the given points -- namely the first one). Plug these values into the equation above and simplify to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=%28-6--5%29%5E2%2B%28-2-1%29%5E2 ALIGN=MIDDLE  ALT=\"r%5E2=%28-6--5%29%5E2%2B%28-2-1%29%5E2\"   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=r%5E2=%28-6%2B5%29%5E2%2B%28-2-1%29%5E2 ALIGN=MIDDLE  ALT=\"r%5E2=%28-6%2B5%29%5E2%2B%28-2-1%29%5E2\"   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=r%5E2=%28-1%29%5E2%2B%28-3%29%5E2 ALIGN=MIDDLE  ALT=\"r%5E2=%28-1%29%5E2%2B%28-3%29%5E2\"   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=r%5E2=1%2B9 ALIGN=MIDDLE  ALT=\"r%5E2=1%2B9\"   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=r%5E2=10 ALIGN=MIDDLE  ALT=\"r%5E2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So because  <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=1 ALIGN=MIDDLE  ALT=\"k=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=10 ALIGN=MIDDLE  ALT=\"r%5E2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the equation of the circle that passes through the points (-6,-2) and (-4,4) (which are the endpoints of the diameter) is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%5E2%2B%28y-1%29%5E2=10 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%5E2%2B%28y-1%29%5E2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%5E2%2B%28y-1%29%5E2=10 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%5E2%2B%28y-1%29%5E2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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