Explanation

(b)
Let mid point of chord of the hyperbola
$\frac{x^{2}}{6} - \frac{y^{2}}{4} = 1\$is
$\left( x_{1},y_{1} \right)$. Therefore equation of chord is
$T = S_{1}$
$\Rightarrow \ \ \frac{xx_{1}}{6} - \frac{yy_{1}}{4} - 1$
$= \frac{x_{1}^{2}}{6} - \frac{y_{1}^{2}}{4} - 1$
$\Rightarrow \ \frac{x_{1}}{6}x - \frac{y_{1}}{4}y$
$= \ \frac{x_{1}^{2}}{6} - \frac{y_{1}^{2}}{4}$
Comparing it with $4x - 3y = 5$, we get$\$
$x_{1} = 2,y_{1} = 1$