document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1041650>Question 1041650</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the smallest distance between the point(–2, –2) and a point on the circumference of the circle given by (x – 1)^2 + (y –2)^2 = 4?<BR>\n" );
document.write( "A) 3<BR>\n" );
document.write( "B) 4<BR>\n" );
document.write( "C) 5<BR>\n" );
document.write( "D) 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #656624 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=656624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The line that passes through the point (-2,-2) and the center (1,2) has equation \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2+=+%28%282--2%29%2F%281--2%29%29%28x-1%29 ALIGN=MIDDLE  ALT=\"y-2+=+%28%282--2%29%2F%281--2%29%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%284%2F3%29x+%2B+2%2F3 ALIGN=MIDDLE  ALT=\"y+=+%284%2F3%29x+%2B+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "after simplifying.\r<BR>\n" );
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document.write( "This line will intersect the circle in two (diametrically) opposite points on the circle, one of which is the farthest from the point (-2,-2), and the other the nearest to the point (-2,-2).\r<BR>\n" );
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document.write( "To find out the points, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%284%2F3%29x+%2B+2%2F3 ALIGN=MIDDLE  ALT=\"y+=+%284%2F3%29x+%2B+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+%2B+%28y-2%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+%2B+%28y-2%29%5E2+=+4\"   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=%28x-1%29%5E2+%2B+%28%284%2F3%29x+%2B+2%2F3-2%29%5E2+=+%28x-1%29%5E2+%2B++%28%284%2F3%29x-4%2F3%29%5E2+=+4 ALIGN=MIDDLE   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=%28x-1%29%5E2+%2B++%2816%2F9%29%28x-1%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+%2B++%2816%2F9%29%28x-1%29%5E2+=+4\"   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=%2825%2F9%29%28x-1%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"%2825%2F9%29%28x-1%29%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+=+36%2F25 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+=+36%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> x = 11/5 or -1/5.\r<BR>\n" );
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document.write( "Incidentally, these are the x-coordinates of the two diametrically opposite points on the circle that are farthest and nearest the point (-2,-2), respectively.  The corresponding y-value is y = 2/5.  The distance of this point (-1/5,2/5) from (-2,-2) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-1%2F5--2%29%5E2%2B%282%2F5--2%29%5E2%29+=+highlight%283%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-1%2F5--2%29%5E2%2B%282%2F5--2%29%5E2%29+=+highlight%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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