Find the equation of tangent to parabola $y^{2} = 4 a x a t (a t^{2}, 2 a t)$

$t y = x + a t^{2}$

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$y = t x + a t^{2}$

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$y a t^{2} = x + t$

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$y + t x = a t^{2}$

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Solution

The correct option is A
$t y = x + a t^{2}$

We are asked to find the equation of the tangent of a parabola in its parametric form. We can use the formula for tangent at a point, $(x_{1}, y_{1}) a s y y_{1} = \frac{4 a (x + x_{1})}{2}$

putting $(x_{1}, y_{1}) = (a t^{2}, 2 a t)$

$y .2 a t = 2 a (x + a t^{2})$

$t y = x + a t^{2}$

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Similar questions

Find the equation of tangent to parabola $y^{2} = 4 a x a t (a t^{2}, 2 a t)$

y^{2} = 4 a x

x^{2} = 4 b x

Find the equation of tangent to parabola $y^{2} = 4 a x a t (a t^{2}, 2 a t)$

x^{2} + y^{2} + 4 a x = 0

y^{2} = 4 a x .

y^{2} = 4 a x

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