If the tangent at the point $\left({\mathrm{at}}^2, {\mathrm{at}}^3\right)$ on the curve ${\mathrm{ay}}^2={\mathrm{x}}^3$ meets the curve again at

$\begin{array}{rcl}\mathrm{a} {\mathrm{y}}^{2={\mathrm{x}}^3} & \Rightarrow & \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{3{\mathrm{x}}^2}{2\mathrm{ay}}=\frac{3({\mathrm{a}}^2 \mathrm{t}4)}{2{\mathrm{a}}^2 {\mathrm{t}}^3}\\ & =& \frac{3\mathrm{t}}{2} \end{array}$

eq of Tangent

$3\mathrm{t} \mathrm{x}-2\mathrm{y}={\mathrm{at}}^3$

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