Q. The parametric coordinates of any point on the parabola $y^{2} = 4ax$ can be
A) $(a - at^{2}, - 2at)$
B) $(a - at^{2},2at)$
C) $(a\sin^{2}t, - 2a\sin t)$
D) $(a\sin^{\ }t, - 2a\cos t)$
Explanation
(c)
If $x = a\sin^{2}t \Rightarrow y^{2} = 4a(a\sin^{2}t)$
$\Rightarrow y = \pm 2a\sin t$
$\therefore$ Option (c) is correct
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.