document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=457962>Question 457962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> URGENT HELP PLEASE!!  Write the equation of the circle that satisfies the stated conditions. In some cases there may be more than one circle that satisfies the conditions. Express the final equation in the form x2 + y2 + Dx + Ey + F = 0.(Objective 1) <BR>\n" );
document.write( "Center at (&#8722;4, &#8722;6)and r = 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #314125 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=314125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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 equation of a circle.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x--4%29%5E2%2B%28y--6%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x--4%29%5E2%2B%28y--6%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4 ALIGN=MIDDLE  ALT=\"h=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-6 ALIGN=MIDDLE  ALT=\"k=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since the center is the point (h,k) ).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x--4%29%5E2%2B%28y--6%29%5E2=%283%29%5E2 ALIGN=MIDDLE  ALT=\"%28x--4%29%5E2%2B%28y--6%29%5E2=%283%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3 ALIGN=MIDDLE  ALT=\"r=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the radius).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x--4%29%5E2%2B%28y--6%29%5E2=9 ALIGN=MIDDLE  ALT=\"%28x--4%29%5E2%2B%28y--6%29%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the radius).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2%2B%28y%2B6%29%5E2=9 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2B%28y%2B6%29%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2%2B%28y%2B6%29%5E2-9=0 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2B%28y%2B6%29%5E2-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 9 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x%2B16%2By%5E2%2B12x%2B36-9=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2B16%2By%5E2%2B12x%2B36-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL and expand.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x%2By%5E2%2B12y%2B43=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2By%5E2%2B12y%2B43=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B8x%2B12y%2B43=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B8x%2B12y%2B43=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms to fit the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2BDx%2BEy%2BF=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2BDx%2BEy%2BF=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The last equation is in standard form. Here we can see that D = 8, E = 12, and F = 43. </SPAN>\n" );
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