<p>A curve \(C\) has equation \(3x^2 + 2xy - 4y^2 = 1\).</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Show that&nbsp;\(\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{3x + y}{4y - x}\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Find the acute angle between the tangent to \(C\) at the point \((1, 1)\) and the \(x\)-axis.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Show that there is no point on \(C\) where the tangent to the curve is parallel to the \(x\)-axis.<span class="inline-marks">[3]</span></div></li></ol>

A curve \(C\) has equation \(3x^2 + 2xy - 4y^2 = 1\).

Show that \(\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{3x + y}{4y - x}\).

Find the acute angle between the tangent to \(C\) at the point \((1, 1)\) and the \(x\)-axis.

Show that there is no point on \(C\) where the tangent to the curve is parallel to the \(x\)-axis.

2024 VJC Promo Q5

2024 VJC Promo Q5