document.write( "Question 1056918: Find the values of k if the line x+y=k is a tangent to the circle x^2+y^2=8 \n" ); document.write( "
Algebra.Com's Answer #671985 by Cromlix(4381)\"\" \"About 
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Hi there,
\n" ); document.write( "x + y = k
\n" ); document.write( "Rearrange
\n" ); document.write( "y = k - x
\n" ); document.write( "Substitute y = k - x
\n" ); document.write( "into:
\n" ); document.write( "x^2 + y^2 = 8
\n" ); document.write( "x^2 + (k - x)^2 = 8
\n" ); document.write( "x^2 + k^2 - 2kx + x^2 = 8
\n" ); document.write( "Collect like terms
\n" ); document.write( "x^2 + x^2 - 2kx + k^2 - 8 = 0
\n" ); document.write( "2x^2 - 2kx + k^2 - 8 = 0
\n" ); document.write( "Using the discriminant b^2 - 4ac
\n" ); document.write( "(-2k)^2 - 4(2)(k^2 - 8) = 0
\n" ); document.write( "4k^2 - 8k^2 + 64 = 0
\n" ); document.write( "-4k^2 + 64 = 0
\n" ); document.write( "-4k^2 = -64
\n" ); document.write( "Divide both sides by -4
\n" ); document.write( "k^2 = 16
\n" ); document.write( "k = √16
\n" ); document.write( "k = 4 and -4
\n" ); document.write( "Hope this helps :-)\r
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