Find the equations of the tangent and normal to the hyperbola $\large {\frac{x^2}{a^2}} -\large { \frac{y^2}{b^2}} =\normalsize 1$ at the $ (x_0, \: y_0)$.

Question

$\begin{array}{1 1} (A)\;\frac{xx_1}{a^2}-\frac{yy_1}{b^2}=1;\frac{y-y_1}{a^2y_1}+\frac{x-x_1}{b^2x_1} = 0 \\ (B)\;\large\frac{xx_1}{a^2}+\frac{yy_1}{b^2}=1;\large\frac{y-y_1}{a^2y_1}+\frac{x-x_1}{b^2x_1}=0 \\ (C)\;\large\frac{xx_1}{a^2}-\frac{yy_1}{b^2}=1;\large\frac{y-y_1}{a^2y_1}-\frac{x-x_1}{b^2x_1}=0 \\ (D)\;\large\frac{xx_1}{a^2}-\frac{yy_1}{b^2}=-1;\large\frac{y-y_1}{a^2y_1}+\frac{x-x_1}{b^2x_1}=0 \end{array} $