| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find tangent equation at point |
| Difficulty | Standard +0.0 This is a standard implicit differentiation question requiring straightforward application of the chain rule to find dy/dx, then substitution of given coordinates to find the tangent equation. It's a typical textbook exercise with no novel insight required, representing average difficulty for A-level. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
\begin{enumerate}
\item A curve has the equation
\end{enumerate}
$$x ^ { 2 } - 3 x y - y ^ { 2 } = 12$$
(i) Find an expression for $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $x$ and $y$.\\
(ii) Find an equation for the tangent to the curve at the point $( 2 , - 2 )$.\\
\hfill \mbox{\textit{OCR C4 Q2 [7]}}