GATE DA 2024 Q22: Equation satisfied by the Fisher linear discriminant

For any binary classification dataset, let $S_B \in \mathbb{R}^{d\times d}$ and $S_W \in \mathbb{R}^{d\times d}$ be the between-class and within-class scatter (covariance) matrices, respectively. The Fisher linear discriminant is defined by $u^* \in \mathbb{R}^d$, that maximizes

$$J(u) = \frac{u^T S_B u}{u^T S_W u}$$

If $\lambda = J(u^*)$, $S_W$ is non-singular and $S_B \neq 0$, then $(u^*, \lambda)$ must satisfy which ONE of the following equations?

Note: $\mathbb{R}$ denotes the set of real numbers.