<p>A curve has parametric equations $x=\frac{4{{t}^{3}}}{3}-t$, $y=t-3{{t}^{2}}$.</p>
<ol class="abc-list"><li data-list-item-id="item-1760866050399-94yudn8ka" data-list-item-path="item-1760866050399-94yudn8ka"><div class="list-item-paragraph">For the part of the curve where&nbsp;$x&gt;0$, find the equation of the tangent to the curve which is parallel to the $y$-axis.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-1760866051134-iow9qjnag" data-list-item-path="item-1760866051134-iow9qjnag"><div class="list-item-paragraph">Find the coordinates of the point where the tangent meets the curve again.<span class="inline-marks">[2]</span></div></li></ol>

A curve has parametric equations $x=\frac{4{{t}^{3}}}{3}-t$, $y=t-3{{t}^{2}}$.

For the part of the curve where $x>0$, find the equation of the tangent to the curve which is parallel to the $y$-axis.

Find the coordinates of the point where the tangent meets the curve again.

2025 YIJC P1 Q4

2025 YIJC P1 Q4

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