Describe briefly the method of Lagrange multipliers for finding the stationary points of a function $f(x, y)$ subject to the constraint $g(x, y)=0$.

Show that at a stationary point $(a, b)$

$$\left|\begin{array}{ll} \frac{\partial f}{\partial x}(a, b) & \frac{\partial g}{\partial x}(a, b) \\ \frac{\partial f}{\partial y}(a, b) & \frac{\partial g}{\partial y}(a, b) \end{array}\right|=0$$

Find the maximum distance from the origin to the curve

$$x^{2}+y^{2}+x y-4=0 .$$