document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581656>Question 581656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the circle passing through the origin and with the center (3,5)\r<BR>\n" );
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document.write( "The answer should be written in the form (x-h) squared + (y-h)squared = radius squared\r<BR>\n" );
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document.write( "Thanks!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371759 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=371759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: the origin is the point (0,0)\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 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-0%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2B%28y-0%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=0 ALIGN=MIDDLE  ALT=\"k=0\"   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=%283-0%29%5E2%2B%285-0%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%283-0%29%5E2%2B%285-0%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=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5 ALIGN=MIDDLE  ALT=\"y=5\"   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=%283%29%5E2%2B%285%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%283%29%5E2%2B%285%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=9%2B25=r%5E2 ALIGN=MIDDLE  ALT=\"9%2B25=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=34=r%5E2 ALIGN=MIDDLE  ALT=\"34=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=0 ALIGN=MIDDLE  ALT=\"k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=34 ALIGN=MIDDLE  ALT=\"r%5E2=34\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the equation of the circle with center (0,0) that goes through the point (3,5) 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-0%29%5E2=34 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2B%28y-0%29%5E2=34\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=34 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=34\"   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=x%5E2%2By%5E2=34 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=34\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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