| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Session | Specimen |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Rectangular hyperbola tangent intersection |
| Difficulty | Challenging +1.2 This is a Further Maths question on rectangular hyperbolas requiring parametric differentiation and solving simultaneous equations. Part (a) is a standard 'show that' requiring implicit differentiation. Part (b) requires substituting the intersection point into two tangent equations and solving the resulting system for two parameter values. While it involves multiple steps and algebraic manipulation, the techniques are standard for F1 and the question structure is predictable for this topic. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
\begin{enumerate}
\item The point $\mathrm { P } \left( 6 \mathrm { t } , \frac { 6 } { \mathrm { t } } \right) , t \neq 0$, lies on the rectangular hyperbola $H$ with equation $x y = 36$ (a) Show that an equation for the tangent to $H$ at $P$ is
\end{enumerate}
$$y = - \frac { 1 } { t ^ { 2 } } x + \frac { 12 } { t }$$
The tangent to $H$ at the point $A$ and the tangent to $H$ at the point $B$ meet at the point $( - 9,12 )$.\\
(b) Find the coordinates of $A$ and $B$.\\
\hfill \mbox{\textit{Edexcel F1 Q7 [12]}}