document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1056900>Question 1056900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value/s of k for which the circle x^2+y^2=4 and (x-4)^2 + (y-3)^2=k^2 intersect at exactly one point. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #671966 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=671966\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Begin making a graph according to this description to help see what you may be able to do:\r<BR>\n" );
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document.write( "Circle centered at origin (0,0) and radius 2;<BR>\n" );
document.write( "Point for other circle center at (4,3), but radius is unknown, k.<BR>\n" );
document.write( "A segment connects the two center points (0,0) and (4,3).  The equation for the LINE for this segment is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F4%29x ALIGN=MIDDLE  ALT=\"y=%283%2F4%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "THINK about that, and the drawing you hopefully made.<BR>\n" );
document.write( "Do you imagine a process to continue and find your k?  <BR>\n" );
document.write( "As a big hint toward that, What is the intersection point for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F4%29x ALIGN=MIDDLE  ALT=\"y=%283%2F4%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=4 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "What is the distance between that found intersection point and (4,3)?<BR>\n" );
document.write( "That would be k.\r<BR>\n" );
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document.write( "I did not solve this for you but explained precisely how you can solve it.\r<BR>\n" );
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document.write( "Solving the nonlinear system  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%283%2F4%29x%2Cx%5E2%2By%5E2=4%29 ALIGN=MIDDLE  ALT=\"system%28y=%283%2F4%29x%2Cx%5E2%2By%5E2=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, omitting the steps for it here, should give you the intersection point, ( 8/5, 6/5 ).  Use the distance formula to find distance from  ( 8/5, 6/5)  to (4,3).  That is your k. </SPAN>\n" );
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