document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114745>Question 1114745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the shortest distance from the origin to a point on the circle defined by x^2 + y^2 &#8722; 6x &#8722; 12y + 41 = 0\r<BR>\n" );
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document.write( "I got as far as (x-6)^2+(y-12)^2 = 5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729655 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=729655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You are not completing the square correctly.  The standard form of the equation for the circle should have (x-3)^2 and (y-6)^2....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+-+6x+-+12y+%2B+41+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+-+6x+-+12y+%2B+41+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9+%2B+y%5E2-12y%2B36+=+-41%2B9%2B36 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9+%2B+y%5E2-12y%2B36+=+-41%2B9%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+%2B+%28y-6%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+%2B+%28y-6%29%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The circle has center (3,6) and radius 2.<br><BR>\n" );
document.write( "The distance from the origin to the center of the circle, by the Pythagorean Theorem, is sqrt(45) = 3*sqrt(5); since the radius of the circle is 2, the shortest distance from the origin to a point on the circle is 3*sqrt(5)-2. </SPAN>\n" );
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