| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Find normal equation |
| Difficulty | Moderate -0.3 This is a standard C4 parametric curves question requiring routine techniques: finding axis intersections by setting x=0 and y=0, recognizing an ellipse for sketching, and finding a normal using dy/dx = (dy/dt)/(dx/dt). The 'show that' format for part (c) provides the answer to verify. All steps are textbook procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
A curve is given parametrically by the equations
$$x = 5 \cos t, \quad y = -2 + 4 \sin t, \quad 0 \leq t < 2\pi$$
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of all the points at which $C$ intersects the coordinate axes, giving your answers in surd form where appropriate. [4]
\item Sketch the graph at $C$. [2]
\end{enumerate}
$P$ is the point on $C$ where $t = \frac{1}{2}\pi$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Show that the normal to $C$ at $P$ has equation
$$8\sqrt{3}y = 10x - 25\sqrt{3}.$$ [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q22 [10]}}