Equation of tangent to the parabola $y^{2} = 4 a x$ in parametric form is

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Solution

Given: Parabola: $y^{2} = 4 a x$
Parametric co-ordinates of the parabola $y^{2} = 4 a x$ are $(a t^{2}, 2 a t) .$
Equation of the tangent to the parabola is $y y_{1} = 2 a (x + x_{1})$

Now replace $(x_{1}, y_{1})$ with parametric co-ordinates.
$∴ y (2 a t) = 2 a (x + a t^{2})$
$\Rightarrow t y = x + a t^{2}$

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