Let $C$ be the point of intersection of the tangent lines $l,\ m$ at A(a,\ a^2),\ B(b,\　b^2)\ (a$y=x^2$ respectively. When $C$ moves on the parabola $y=\frac 12x^2-x-2$, find the minimum area bounded by 2 lines $l,\ m$ and the parabola $y=x^2$.