document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203857>Question 203857</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me about this :<BR>\n" );
document.write( "Find R so that the circle x^2+y^2=R^2 is tangent to the line x+2y=4.<BR>\n" );
document.write( "Thanx:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153812 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=153812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find R so that the circle x^2+y^2=R^2 is tangent to the line x+2y=4.<BR>\n" );
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document.write( "The center of the circle is the Origin.  A line from the center to the tangent point will be perpendicular to the line x+2y=4.  See that? Since it's perpendicular, its slope will be the negative inverse of the line, and it passes thru the origin.<BR>\n" );
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document.write( "Find the slope of x+2y=4 by putting it into slope-intercept form (that means solve for y).<BR>\n" );
document.write( "y = (-1/2)x + 2 so the slope, m, is -1/2.<BR>\n" );
document.write( "The slope of the line from the center, the Origin, to the tangent point will have a slope of +2.<BR>\n" );
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document.write( "Use y-y1 = m*(x-x1) to find the eqn of the radial line.<BR>\n" );
document.write( "y = 2x since the point is (0,0)<BR>\n" );
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document.write( "Now solve the pair of eqns to find the tangent point.<BR>\n" );
document.write( "x + 2y = 4<BR>\n" );
document.write( "y = 2x<BR>\n" );
document.write( "x + 2*(2x) = 4<BR>\n" );
document.write( "5x = 4<BR>\n" );
document.write( "x = 0.8<BR>\n" );
document.write( "y = 1.6<BR>\n" );
document.write( "The tangent point is (0.8,1.6).<BR>\n" );
document.write( "The radius, R, is the distance from the Origin to the point.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2+=+0.8%5E2+%2B+1.6%5E2 ALIGN=MIDDLE  ALT=\"R%5E2+=+0.8%5E2+%2B+1.6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2+=+3.2 ALIGN=MIDDLE  ALT=\"R%5E2+=+3.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "R = sqrt(3.2) = 4*sqrt(5)/5<BR>\n" );
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