| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2024 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola area calculations |
| Difficulty | Standard +0.8 This is a Further Maths question requiring implicit differentiation of a rectangular hyperbola, finding tangent equations, determining intercepts, and using area constraints. While the techniques are standard for F1, the multi-step nature, parametric point representation, and algebraic manipulation required place it moderately above average difficulty. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
\begin{enumerate}
\item The hyperbola $H$ has equation $x y = c ^ { 2 }$ where $c$ is a positive constant.
\end{enumerate}
The point $P \left( c t , \frac { c } { t } \right)$, where $t > 0$, lies on $H$.\\
The tangent to $H$ at $P$ meets the $x$-axis at the point $A$ and meets the $y$-axis at the point $B$.\\
(a) Determine, in terms of $c$ and $t$,\\
(i) the coordinates of $A$,\\
(ii) the coordinates of $B$.
Given that the area of triangle $A O B$, where $O$ is the origin, is 90 square units,\\
(b) determine the value of $c$, giving your answer as a simplified surd.
\hfill \mbox{\textit{Edexcel F1 2024 Q3 [6]}}