Find the equation of tangent to parabola y 2-4 ax at at 2- 2 at A- t y-x-a t2B- y-t x-a t2C- y-t x-a t2D- y a t2-x-t

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Question

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

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Solution

The correct option is A

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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Find the equation of tangent to parabola y2=4ax at(at2,2at)

The correct option is A 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,(x1,y1)as yy1=4a(x+x1)2 putting (x1,y1)=(at2,2at) y.2at=2a(x+at2) ty=x+at2

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