<p>A curve $C$ has equation ${{\left( \ln y \right)}^{2}}-3xy+{{x}^{2}}-4=0$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\left( 3y-2x \right)y}{2\ln y-3xy}$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">It is given that $C$ contains the point $A$ with coordinates $\left( \alpha ,1 \right)$ where $\alpha <0$.</span></div><div class="list-item-paragraph">Find the value of $\alpha $ and hence the equation of the normal to $C$ at the point $A$.</div><p style="text-align: right;">[3]</p></li></ol>

A curve $C$ has equation ${{\left( \ln y \right)}^{2}}-3xy+{{x}^{2}}-4=0$.

Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\left( 3y-2x \right)y}{2\ln y-3xy}$.

It is given that $C$ contains the point $A$ with coordinates $\left( \alpha ,1 \right)$ where $\alpha <0$.

Find the value of $\alpha $ and hence the equation of the normal to $C$ at the point $A$.

2019 ASRJC Promo Q3

2019 ASRJC Promo Q3

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