document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1017503>Question 1017503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi!\r<BR>\n" );
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document.write( "What are the equations of the lines through (8,-3) and passing at distance &#8730;10 from (3,2)?\r<BR>\n" );
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document.write( "I've answered all my homework except this.<BR>\n" );
document.write( "Please help! Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #633786 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52790)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=633786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Hi!\r<BR>\n" );
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document.write( "What are the equations of the lines through (8,-3) and passing at distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from (3,2)?\r<BR>\n" );
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document.write( "I've answered all my homework except this.<BR>\n" );
document.write( "Please help! Thanks!<BR>\n" );
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document.write( "I'd solve this problem in this way:\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "1. The equation of a straight line passing through (8,-3) is\r\n" );
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document.write( "   y + 3 = m*(x-8),          (1)\r\n" );
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document.write( "   where m is a parameter, now unknown.\r\n" );
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document.write( "2. The equation of the given circle is \r\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+%2B+%28y-2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+%2B+%28y-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   (2)\r\n" );
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document.write( "3. Now substitute the expression  y = m*(x-8)-3  from (1) into equation (2) and find the coefficient m \r\n" );
document.write( "   under the condition that the obtained quadratic equation has only one real root.\r\n" );
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document.write( "   This requirement means that the straight line is tangent to the circle and, hence, lies at the distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from its center.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Now my question is: is this advice enough for you?\r<BR>\n" );
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document.write( "Can you complete the solution yourself?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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