<p>The curve \(C\) has equation \(x^3 + y^3 - 3xy = k\), where \(k\) is a positive constant. \(C\) intersects the \(x\)-axis at the point \(A\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the equation of the tangent to \(C\) at \(A\). Give your answer in the form \(y = px + q\), where \(p\) and \(q\) are constants to be found in terms of \(k\).</span><span class="inline-marks">[5]</span></div></li><li><div class="list-item-content"><span class="list-item-text">There are two points on \(C\) where the tangents are parallel to the \(y\)-axis. Given that \(k = 3\), find the exact \(y\)-coordinates of these two points.</span><span class="inline-marks">[3]</span></div></li></ol>

The curve \(C\) has equation \(x^3 + y^3 - 3xy = k\), where \(k\) is a positive constant. \(C\) intersects the \(x\)-axis at the point \(A\).

Find the equation of the tangent to \(C\) at \(A\). Give your answer in the form \(y = px + q\), where \(p\) and \(q\) are constants to be found in terms of \(k\).

There are two points on \(C\) where the tangents are parallel to the \(y\)-axis. Given that \(k = 3\), find the exact \(y\)-coordinates of these two points.

2025 EJC P2 Q1

2025 EJC P2 Q1