For the curve x=t2−1,y=t2−t, the tangent is perpendicular to x-axis then

x=t2−1,  y=t2−t Slope of tangent=(dydx)0=2t−12t=1−12t ∴ Tangent is ⊥lar to x− axis⇒ slope of tangent=∞ ⇒ 1−12t=∞  ⇒t=0