This solution will guide you through finding the equation of the normal to a hyperbola at a given point and then determining which of the provided options lies on that normal.

Key Concept: Equation of the Normal to a Hyperbola

For a hyperbola centered at the origin with its equation given in the standard form: $\frac{x^2}{A^2} - \frac{y^2}{B^2} = 1$ the equation of the normal line at a point $P(x_1, y_1)$ lying on the hyperbola is given by: $\frac{A^2x}{x_1} + \frac{B^2y}{y_1} = A^2 + B^2$

**Derivation