Explanation

(c)
Given, $x = t^{2} + 2t - 1$ …(i)
and $y = 3t + 5 \Rightarrow t = \frac{y - 5}{3}\$ …(ii)
On putting the value of $t$ in Eq. (i), we get
$x = \left( \frac{y - 5}{3} \right)^{2} + 2\left( \frac{y - 5}{3} \right) - 1$
$\Rightarrow \ x = \frac{1}{9}\left\{ y^{2} - 4y - 14 \right\}$
$\Rightarrow \ (y - 2)^{2} = 9(x + 2)$
This is an equation of a parabola