Question

The parametric coordinates of any point on the parabola $y^2=4 a x$ can be

(a) $\left(a-a t^2,-2 a t\right)$

(b) $\left(a-a t^2, 2 a t\right)$

(c) $\left(a \sin ^2 t,-2 a \sin t\right)$

(d) $(a \sin t,-2 a \cos t)$

Answer 1

$\text { Let }  x=a \sin ^2 t, y=-2 a \sin t \\$

$\because  y^2=4 a x \\$

$\Rightarrow  (-2 a \sin t)^2=4 a^2 \sin ^2 t \\$

$\Rightarrow  4 a^2 \sin ^2 t=4 a^2 \sin ^2 t$

So, The correct option of this question will be (C).