Question

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

• A. $(a,a)$
• B. $(0,a)$
• C. $(0,0)$
• D. $(a,0)$

Answer 1

The correct option is C $(0,0)$

We have, $x=a{t}^2\Rightarrow \frac{dx}{dt}=2at$

And $y=2at\Rightarrow \frac{dy}{dt}=2a$

$\therefore \frac{dy}{dx}=\frac{1}{t}=\infty$, for tangent to the curve perpendicular to $x-$axis

$\Rightarrow t=0$

so the point of contact is $(a{t}^2,2at)=(0,0)$