| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find normal equation at point |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question requiring standard application of the product and chain rules, followed by routine calculation of a normal line. While it involves multiple steps, the techniques are mechanical and commonly practiced in C4, making it slightly easier than average. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
A curve has the equation
$$x^2 + 3xy - 2y^2 + 17 = 0.$$
\begin{enumerate}[label=(\roman*)]
\item Find an expression for $\frac{dy}{dx}$ in terms of $x$ and $y$. [4]
\item Find an equation for the normal to the curve at the point $(3, -2)$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C4 Q2 [7]}}