What are the parametric equations of the para | vedclass

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Question

(A) The given equation of the parabola is $(y - 2)^2 = 12(x - 4)$.Comparing this with the standard form $(y - k)^2 = 4a(x - h)$,we get $h = 4$,$k = 2$

Vedclass · Accepted Answer

$x = 4 + 3t^2, y = 2 + 6t$

Vedclass · Answer

(A) The given equation of the parabola is $(y - 2)^2 = 12(x - 4)$.Comparing this with the standard form $(y - k)^2 = 4a(x - h)$,we get $h = 4$,$k = 2$,and $4a = 12$,which implies $a = 3$.The parametric equations for a parabola of the form $(y - k)^2 = 4a(x - h)$ are given by $x = h + at^2$ and $y = k + 2at$.Substituting the values $h = 4$,$k = 2$,and $a = 3$:$x = 4 + 3t^2$$y = 2 + 2(3)t = 2 + 6t$Thus,the parametric equations are $x = 4 + 3t^2$ and $y = 2 + 6t$.

What are the parametric equations of the parabola $(y - 2)^2 = 12(x - 4)$?

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