If the tangent to the curve `x=a\ t^2,\ \ y=2a t` is perpendicular to x-axis, then its point of contact is `(a ,\ a)` (b) `(0,\ a)` (c) `(0,\ 0)` (d) `(a ,\ 0)`

Explanation

Given,`x = at^2, y = 2at`


When tangent to the curve is perpendicular to x-axis, then `dy / dx = ∞.`


`dx / dt = 2at `and `dy / dt = 2a`


`dy / dx = [dy / dt ] * [dt / dx] = 2a / 2at = ∞`


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