A tangent to the curve x = a t^{2}, y = 2 a t | vedclass

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(B) The given parametric equations $x = a t^{2}$ and $y = 2 a t$ represent the parabola $y^{2} = 4 a x$.If the tangent is perpendicular to the $X$-axi

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$(0, 0)$

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(B) The given parametric equations $x = a t^{2}$ and $y = 2 a t$ represent the parabola $y^{2} = 4 a x$.If the tangent is perpendicular to the $X$-axis,it must be a vertical line.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,its slope must be undefined,which occurs when $t = 0$.Substituting $t = 0$ into the parametric equations:$x = a(0)^{2} = 0$$y = 2a(0) = 0$Thus,the point of contact is $(0, 0)$.

$A$ tangent to the curve $x = a t^{2}, y = 2 a t$ is perpendicular to the $X$-axis. Then the point of contact is:

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