<p>A curve $C$ has parametric equations</p>
<p style="text-align: center">$x=2+t+\frac{2}{t}$,  $\qquad\qquad$  $y=2-t+\frac{2}{t}$,</p>
<p>where&nbsp;$t$< 0.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $t$ and hence find the exact value of $t$ for which the tangent to the curve at $t$ is parallel to the $y$-axis.</div></li><li><div class="list-item-paragraph">Find the value of $t$ for which the distance from the point $(1, 0)$ to the curve is the shortest possible.</div></li></ol>

$x=2+t+\frac{2}{t}$,  $\qquad\qquad$  $y=2-t+\frac{2}{t}$,

Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $t$ and hence find the exact value of $t$ for which the tangent to the curve at $t$ is parallel to the $y$-axis.

Find the value of $t$ for which the distance from the point $(1, 0)$ to the curve is the shortest possible.

2013 ACJC P2 Q3 [Modified]

2013 ACJC P2 Q3 [Modified]

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