document.write( "Question 1056900: 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. \n" ); document.write( "

Algebra.Com's Answer #671971 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "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.
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\n" ); document.write( "\n" ); document.write( "There are two answers: k = 3 and k = 7.\r
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document.write( "1.  x^2+y^2=4  is the circle of the radius 2 with the center at the origin (0,0).\r\n" );
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document.write( "2.  (x-4)^2 + (y-3)^2=k^2  is the circle of the radius \"k\" with the center at the point (4,3).\r\n" );
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document.write( "    Notice that this center lies at the distance 5 =  from the origin.\r\n" );
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document.write( "3.  The condition requires that the circle #1 touches the circle #2.\r\n" );
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document.write( "    It is possible in two cases:\r\n" );
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document.write( "    k = 5 - 2 = 3  (exterior touching),  and'\r\n" );
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document.write( "    k = 5 + 2 = 7  (interior touching).\r\n" );
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