find the equation of the tangent to the parabola x=2at, y=at^2 the point where t=3

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pramodpandey | College Teacher | (Level 3) Valedictorian

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convert equation in cartesian form ,we have

`x=2at ,y=at^2`


`t^2=x^2/(4a^2)`  ,substitute  in y

we have


`x^2=4ay`                (i)

differentiate (i) with respect to x,



`(dy)/(dx)}_ t=(2at)/(2a)=t`

Equation of the tangents at 't'





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