Explanation

(d)
Given, $\frac{x}{a} = \left( t + \frac{1}{t} \right)$ and $\frac{y}{b} = \left( t - \frac{1}{t} \right)$
$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = \left( t + \frac{1}{t} \right)^{2} - \left( t - \frac{1}{t} \right)^{2} = 4$
$\Rightarrow \ \frac{x^{2}}{4a^{2}} - \frac{y^{2}}{4b^{2}} = 1$