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Question

If the tangent to the curve x = a t2, y = 2 at is perpendicular to x-axis, then its point of contact is

(a) (a, a)
(b) (0, a)
(c) (0, 0)
(d) (a, 0)

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Solution

(c) (0, 0)

Let the required point be (x1, y1).

Since, the point lies on the curve.Hence, x1=at2 and y1=2atNow, x=at2 and y=2atdxdt=2at and dydt=2adydx=dydtdxdt=2a2at=1t=2aySlope of the tangent = dydxx1, y1=2ay1It is given that the tangent is perpendicular to the y-axis.It means that it is parallel to the x-axis.∴ Slope of the tangent = Slope of the x-axis2ay1=0a=0Now, x1=at2=0 and y1=2at=0x1, y1=0, 0

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