2026 RI Promo Q4

2026 RI Promo Q4

Junior College 1
7 marks

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

  1. Use calculus to find the exact equations of tangents to \(C\) that are parallel to the \(x\)-axis.[4]
  2. Show that \(C\) is symmetrical about the line \(y=x\). Hence write down the equations of tangents to \(C\) that are parallel to the \(y\)-axis.[2]
  3. Describe geometrically the region enclosed by the tangents found in parts (a) and (b).[1]

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Answer:(a) \(y=0,\ y=\sqrt[3]4\). (b) \(x=0,\ x=\sqrt[3]4\). (c) A square of side \(\sqrt[3]4\).

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