<p>A curve ${{C}_{1}}$ has parametric equations</p>
<p style="text-align: center">$x=at\left( t+2 \right)$,  $\qquad$  $y=a\left( {{t}^{2}}+1 \right)$ $\qquad$  where&nbsp;$a$ is a positive constant.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find, in terms of $a$, the equation of the normal to the curve at the point where&nbsp;$t=\frac{1}{2}$.<span class="inline-marks">[3]</span></div></li></ol>
<p>Another curve ${{C}_{2}}$ has equation ${{\mathrm{e}}^{3x}}+{{\mathrm{e}}^{y}}=4$.</p>
<ol class="abc-list" start="2"><li><div class="list-item-paragraph">Given that the normal in part <strong>(a)</strong> is also tangent to ${{C}_{2}}$ at a point, find the exact value of $a$.<span class="inline-marks">[4]</span></div></li></ol>

A curve ${{C}_{1}}$ has parametric equations

$x=at\left( t+2 \right)$,  $\qquad$  $y=a\left( {{t}^{2}}+1 \right)$ $\qquad$  where $a$ is a positive constant.

Find, in terms of $a$, the equation of the normal to the curve at the point where $t=\frac{1}{2}$.

Another curve ${{C}_{2}}$ has equation ${{\mathrm{e}}^{3x}}+{{\mathrm{e}}^{y}}=4$.

Given that the normal in part (a) is also tangent to ${{C}_{2}}$ at a point, find the exact value of $a$.

Given that the normal in part **(a)** is also tangent to ${{C}_{2}}$ at a point, find the exact value of $a$.

2022 EJC Promo Q3

2022 EJC Promo Q3

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