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# Find the tangent at the parametric coordinate of parabola $y^2=4ax$?

$\begin{array}{1 1}(a)\;ty=x+at^2\\(b)\;2ty=x+at\\(c)\;tx=y+at^2\\(d)\;ty^2=x+at\end{array}$

For the parabola $y^2=4ax$ parametric coordinate are $(at^2,2at)$ hence supposing a point $(x_1,y_1)$ at the parabola.
Equation of tangent at the parabola $y^2=4ax$ is $yy_1=2a(x+x_1)$
Hence at point $(at^2,2at)$ is
$y\times 2at=2a(x+at^2)$
$ty=x+at^2$
Hence (a) is the correct answer.