Calculus

If $z = f(x, y)$ where $x = r \cos\theta$ and $y = r \sin\theta$, given: $\left( \frac{\partial z}{\partial x} \right)^2 + \left( \frac{\partial z}{\partial y} \right)^2 = k \left[ \left( \frac{\partial z}{\partial r} \right)^2 + \frac{1}{r^2} \left( \frac{\partial z}{\partial \theta} \right)^2 \right]$ The value of $k$ is ________ (answer in integer).