A tangent line is drawn to the hyperbola $xy= 1$ at a point $\displaystyle P=\left(2,\ \frac{1}{2}\right)$. Find the midpoint $M$ of the line segment cut from this tangent line by the coordinate axis.

Note: It turns out that the triangle formed by the tangent line and the coordinate axes always has the same area, no matter where $P$ is located on the hyperbola.

$x(M)=$     $y(M)=$