Find the values of $k$ for which the line $y=kx+1$ is a tangent to the curve $y=x^2-7x+2$.

Find the values of $k$ for which the $x-$axis is a tangent to the curve $y=x^2-(k+3)x+(3k+4)$.

Find the value of $k$ for which the line $x+ky=12$ is a tangent to the curve $y=\frac{5}{x-2}$.

Find the values of $m$ for which the line $y=mx+6$ is a tangent to the curve $y=x^2-4x+7$. For each of these values of $m$, find the coordinates of the point where the line touches the curve.

Find the set of values of $k$ for which the line $y=2x-1$ intersects the curve $y=x^2+kx+3$ at two distinct points.

Find the set of values of $k$ for which the line $x+2y=k$ intersects the curve $xy=6$ at two distinct points.

Find the set of values of $k$ for which the line $y=k-x$ cuts the curve $y=5-3x-x^2$ at two distinct points.

Find the set of values of $m$ for which the line $y=mx+5$ not meet the curve $y=x^{2}-x+6$.

Find the set of values of $k$ for which the line $y=2x-10$ does not meet the curve $y=x^2-6x+k$.