Explanation

(c)
Given equation of curve is
$y^{2} - x^{2} + 2x - 1 = 0$
Here, $a = - 1,\ b = 1,\ c = - 1,\ h = 0,\ g = 1,\ f = 0$
$\therefore\ \mathrm{\Delta} = abc + 2fgh - {af}^{2} - {bg}^{2} - {ch}^{2}$
$= ( - 1)(1)( - 1) + 2(0)1(0) - 0 - 1 - 0$
$= 1 - 1 = 0$
$\therefore\$Given equation is equation of pair of straight lines.