If the tangent at the point \( \left(a t^{2}, a t^{3}\right) \) on the curve \( a y^{2}=x^{3} \)...

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If the tangent at the point \( \left(a t^{2}, a t^{3}\right) \) on the curve \( a y^{2}=x^{3} \) meets the curve again at \( \mathrm{P} \) then \( \mathrm{P} \) is
(a) \( \left(\frac{a t^{2}}{4},-\frac{a t^{3}}{8}\right) \)
(b) \( \left(-\frac{a t^{2}}{4}, \frac{a t^{3}}{8}\right) \)
(c) \( \left(\frac{a t^{2}}{4}, \frac{a t^{3}}{8}\right) \)
(d) \( \left(-\frac{a t^{2}}{4},-\frac{a t^{3}}{8}\right) \)
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