2002 AMC 10B Problem 12

For which of the following values of k does the equation \frac{x-1}{x-2} = \frac{x-k}{x-6} have no solution for x?

\textbf{(A) } 1\qquad \textbf{(B) } 2\qquad \textbf{(C) } 3\qquad \textbf{(D) } 4\qquad \textbf{(E) } 5

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.