If tangent tto the curve `x=at^(2),y=2at` is perpendicular to X-axis, then its pointt of contact is

Options

A. `(a,a)`
B. `(0,a)`
C. `(0,0)`
D. `(a,0)`

Answer

C

Explanation

Given `x = at^(2)`
and `y = 2at`
`therefore (dx)/(dt) = 2at`
and `(dy)/(dt) = 2a`
`therefore ` Slope of tangent,
`((dy)/(dt)) = (2a)/(2at) = (1)/(t)`
`therefore` Tangent is perpendicular to X - axis.
`because " "(1)/(t) = oo`
`rArr" " t = 0`
`therefore` Point of contact is (0,0)