Finding Riemannian metric from this geodesic

Question

In a $d$-dimensional Riemannian manifold, given a geodesic equation $\gamma^i(t)=a^i\phi(tb^i),i\in 1\ldots d$, where $\phi:\mathbb{R}\rightarrow\mathbb{R}$ is an increasing function, $a^i,b^i$ are constants, is it possible to determine a Riemannian metric (and the corresponding Christoffel symbols) that derives such a geodesic?