| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find stationary points |
| Difficulty | Standard +0.8 This question requires implicit differentiation to find dy/dx, setting it to zero for stationary points, then solving the resulting system of equations with the original curve equation. While implicit differentiation is standard C4 content, the algebraic manipulation of the simultaneous equations (one quadratic, one from dy/dx = 0) and handling the xy term makes this more challenging than routine differentiation questions. |
| Spec | 1.07s Parametric and implicit differentiation |
6 A curve is defined by the equation $9 x ^ { 2 } - 6 x y + 4 y ^ { 2 } = 3$.
Find the coordinates of the two stationary points of this curve.\\
\hfill \mbox{\textit{AQA C4 2012 Q6 [8]}}