If tangent to the curve x = at2, y = 2at is perpendicular to x-axis then its point of contact is

(a, a) (0, a) (a, 0) (0, 0)

(0, 0)

$\frac{d x}{d t}=2 a t, \frac{d y}{d t}=2 a \Rightarrow \frac{d y}{d x}=\frac{2 a}{2 a t}=\frac{1}{t}$ $\Rightarrow \frac{1}{t}=\infty$  ⇒  t = 0  ⇒  Point is (0,0)