document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970828>Question 970828</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for what value(s) of m is the line y = mx + 5 at a distance 4 from the origin? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593466 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> for what value(s) of m is the line y = mx + 5 at a distance 4 from the origin?<BR>\n" );
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document.write( "All points on a circle about the Origin with r = 4 are 4 units from the Origin.<BR>\n" );
document.write( "Find the intersections of <BR>\n" );
document.write( "y = mx + 5 and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+=+16 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28mx%2B5%29%5E2+=+16 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28mx%2B5%29%5E2+=+16\"   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%2A%28m%5E2+%2B+1%29+%2B+10mx+%2B+9+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2A%28m%5E2+%2B+1%29+%2B+10mx+%2B+9+=+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+=+-5m%2F%28m%5E2%2B1%29+%2B+sqrt%28100m%5E2+-+36%28m%5E2%2B1%29%29%2F%282%28m%5E2%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That doesn't look promising.<BR>\n" );
document.write( "Try this:<BR>\n" );
document.write( "The slope at any point on the circle is -x/y.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = mx + 5<BR>\n" );
document.write( "m = (y-5)/x = -x/y<BR>\n" );
document.write( "x^2 = -y^2 + 5y --> x^2 + y^2 = 5y<BR>\n" );
document.write( "5y = 16<BR>\n" );
document.write( "y = 3.2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2 + y^2 = 16<BR>\n" );
document.write( "x^2 = 16 - 3.2^2 = 5.76<BR>\n" );
document.write( "x = -2.4, +2.4<BR>\n" );
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document.write( "The 2 tangent points are (-2.4,3.2) and (2.4,3.2)<BR>\n" );
document.write( "The y-int of y = mx + 5 is (0,5)<BR>\n" );
document.write( "1 slope = (5-3.2)/2.4 = +0.75<BR>\n" );
document.write( "The other is -0.75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );