Let $y \in \mathbb{R}^n$, $X \in \mathcal{S}^n_{++}(\mathbb{R})$. Why would function $ f : (X, y) \mapsto y^T X^{-1} y$ be convex?

I tried with $(X, x) + t.(Y, y)$ with no result. Also, I thought about using the eigenvalues of $X$, without result. Do you have any idea?