Normal of curvature of curves in a surface

Question

Let be $ S=\{ (x,y,z) \in \mathbb{R}^3| z=y^2-3x^2 \} $

1. Determine the normal curvature at time $t=0$ of curves parametrized by arc length $ \gamma: (-1,1)->S$ with $\gamma(0)=(0,0,0)$

2. Find two regular curves $\gamma_1, \gamma_2$ such that their reparametrizations by arc length have the minimum and maximum normal curvature

I have to use the Euler formula i.e. the normal curvature of a curve on the surface is $k_1cos^2(\theta)+k_2sin^2(\theta)$ or the formula $<N((0,0,0)),\gamma''(0)>$ where $n$ is the gauss map? And for the minimum and maximum normal curvature, do I need to find principal directions?