Equation of normal at $(x_1,y_1)$ is
$\large\frac{a^2x}{x_1}-\frac{b^2y}{y_1}$$=a^2-b^2$
Parametric coordinate $(x_1,y_1)$ is $(a\cos\theta,b\sin\theta)$
Hence $\large\frac{a^2x}{a\cos \theta}-\frac{b^2y}{b\sin \theta}$$=a^2-b^2$
$\large\frac{ax}{\cos\theta}-\frac{by}{\sin \theta}\normalsize =a^2-b^2$
Hence (a) is the correct answer.