document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=530466>Question 530466</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of a circle given its center C and one point P.\r<BR>\n" );
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document.write( "C(0,4),P(0,0).\r<BR>\n" );
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document.write( "Thank You! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350059 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=350059\">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-0%29%5E2%2B%28y-4%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2B%28y-4%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=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=4 ALIGN=MIDDLE  ALT=\"k=4\"   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=%280-0%29%5E2%2B%280-4%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%280-0%29%5E2%2B%280-4%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=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the point that lies on the circle, which is in the form (x,y) ).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%29%5E2%2B%28-4%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%280%29%5E2%2B%28-4%29%5E2=r%5E2\"   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=0%2B16=r%5E2 ALIGN=MIDDLE  ALT=\"0%2B16=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square each term.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=r%5E2 ALIGN=MIDDLE  ALT=\"16=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add.\r<BR>\n" );
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document.write( "So because  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=4 ALIGN=MIDDLE  ALT=\"k=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=16 ALIGN=MIDDLE  ALT=\"r%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the equation of the circle with center (0,4) that goes through the point (0,0) is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0%29%5E2%2B%28y-4%29%5E2=16 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2B%28y-4%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "which simplifies to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28y-4%29%5E2=16 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28y-4%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Jim<BR>\n" );
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