The parametric coordinates of any point on the parabola y2 = 4ax are given by

Question

The parametric coordinates of any point on the parabola y2 = 4ax are given by (A)  (-at2, 2at)  (B)  (a sin2t,-2a sin t)  (C)  (-at2- 2at)  (D)  (a sin t,-2a sin t )

Tardigrade Admin · Accepted Answer

Given curve is y2=4 a x. Taking option (b), At point (a sin 2 t,-2 a sin t), (-2 a sin t)2 =4 a(a sin 2 t) ⇒ 4 a2 sin 2 t =4 a2 sin 2 t

Q. The parametric coordinates of any point on the parabola $y^{2} = 4 a x$ are given by

$(- a t^{2}, 2 a t)$

$(a sin^{2} t, - 2 a sin t)$

$(- a t^{2} - 2 a t)$

$(a sin t, - 2 a sin t$ )

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

Q. The parametric coordinates of any point on the parabola y2=4ax are given by

(−at2,2at)

(asin2t,−2asint)

(−at2−2at)

(asint,−2asint )