Question

The parametric coordinates of any point on the parabola $ y^2 = 4ax $ are given by

• A. $ (-at^2, 2at) $
• B. $ (a\,\sin^2t,-2a\,\sin\,t) $
• C. $ (-at^2- 2at) $
• D. $ (a \, \sin t,-2a \,\sin\,t $ )

Answer 1

Answer: (B)

Given curve is $y^{2}=4 a x$.
Taking option (b),
At point $\left(a \sin ^{2} t,-2 a \sin t\right)$,
$(-2 a \sin t)^{2} =4 a\left(a \sin ^{2} t\right) $
$ \Rightarrow 4 a^{2} \sin ^{2} t =4 a^{2} \sin ^{2} t$