If the tangent to the curve x = at^2, y = 2at | vedclass

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(A) Given the parametric equations of the curve: $x = at^2$ and $y = 2at$.First,find the derivatives with respect to $t$:$\frac{dx}{dt} = 2at$ and $\f

Vedclass · Accepted Answer

$(0, 0)$

Vedclass · Answer

(A) Given the parametric equations of the curve: $x = at^2$ and $y = 2at$.First,find the derivatives with respect to $t$:$\frac{dx}{dt} = 2at$ and $\frac{dy}{dt} = 2a$.The slope of the tangent is given by $\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{2a}{2at} = \frac{1}{t}$.For the tangent to be perpendicular to the $x$-axis,the slope must be undefined (i.e.,$\frac{dy}{dx} 	o \infty$).This occurs when the denominator $t = 0$.Substituting $t = 0$ into the parametric equations:$x = a(0)^2 = 0$$y = 2a(0) = 0$Therefore,the point of contact is $(0, 0)$.

If the tangent to the curve $x = at^2, y = 2at$ is perpendicular to the $x$-axis,then what is the point of contact?

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