The gradient of $f(x,y) = x^2 + y^4$ is tangent to the curve $\gamma(t)=(t^2,t)$, at a point $P = \gamma(t_0)$, with $t_0 > 0$. Consider the level curve of $f$ that contains $P$. Find the equation of the tangent line to this curve at point $P$.
What I got from the question is:
1) The gradient vector is perpedincular to the direction vector of the line I'm trying to find;
2) The gradient vector is parallel to the derivative of $\gamma(t_0)$
But I think I'm missing something to continue.