If tangent to the curve $x = at^{2},\ y = 2at$ is perpandicular to $x$-axis, then its point of contact is

Question

Dr. Abubacker · Accepted Answer

(c)
Given, $x = at^{2}$ and $y = 2at$
$	herefore\ \ \ \ \frac{dx}{dt} = 2at$ and $\frac{dy}{dt} = 2a$
$	herefore$ Slope of tangent, $\left( \frac{dy}{dx} ight) = \frac{2a}{2at} = \frac{1}{t}$
$\Rightarrow \ \ \frac{1}{t} = \infty,\ \ \  \Rightarrow \ \ \ \ \ t = 0$ [given]
$	herefore$ Point of contact is (0, 0)

Q. If tangent to the curve $x = at^{2},\ y = 2at$ is perpandicular to $x$-axis, then its point of contact is

Explanation

Reviewed by Dr. Abubacker

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