| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2023 |
| Session | October |
| Marks | 12 |
| Topic | Implicit equations and differentiation |
| Type | Find vertical tangent points |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question requiring standard technique to find dy/dx, then solving for when the tangent is vertical (dy/dx undefined). The algebra is routine and the question clearly guides students through both steps with no novel insight required. |
| Spec | 1.07s Parametric and implicit differentiation |
\begin{enumerate}
\item A curve is described by the equation
\end{enumerate}
$$x ^ { 2 } + 4 x y + y ^ { 2 } + 27 = 0$$
(a) Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $x$ and $y$.
A point $Q$ lies on the curve.\\
The tangent to the curve at $Q$ is parallel to the $y$-axis.\\
Given that the $x$ coordinate of $Q$ is negative,\\
(b) use your answer to part (a) to find the coordinates of $Q$.\\[0pt]
\\
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q1 [12]}}