The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4 x$, is

The solution for minimizing the function $\mathrm{z}=x+y$ under an L.P.P. with constraints $x+y \geq 2, x+2 y \leq 8, y \leq 3, x, y \geq 0$ is

The angle between lines whose direction cosines satisfy the equation $l+m+n=0$ and $l^2-\mathrm{m}^2-\mathrm{n}^2=0$, is

The circumcenter of the triangle formed by lines $x y+2 x+2 y+4=0$ and $x+y+2=0$ is