| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2021 |
| Session | January |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Find intersection points |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring substitution of parametric equations into a Cartesian equation, finding a normal using dy/dx, and solving simultaneous equations. All techniques are standard with no novel insight required, though the multi-step nature and Further Maths context place it slightly above average A-level difficulty. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.03h Parametric equations: in modelling contexts1.07s Parametric and implicit differentiation |
\begin{enumerate}
\item The hyperbola $H$ has Cartesian equation $x y = 25$
\end{enumerate}
The parabola $P$ has parametric equations $x = 10 t ^ { 2 } , y = 20 t$\\
The hyperbola $H$ intersects the parabola $P$ at the point $A$\\
(a) Use algebra to determine the coordinates of $A$
The point $B$ with coordinates $( 10,20 )$ lies on $P$\\
(b) Find an equation for the normal to $P$ at $B$
Give your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers to be determined.\\
(c) Use algebra to determine, in simplest form, the exact coordinates of the points where this normal intersects the hyperbola $H$\\
(6)
\hfill \mbox{\textit{Edexcel F1 2021 Q8 [14]}}