| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Rectangular hyperbola normal re-intersection |
| Difficulty | Standard +0.8 This is a Further Maths question on rectangular hyperbolas requiring parametric verification (routine), normal equation derivation (standard differentiation), and finding a re-intersection point (solving a quartic via substitution). The re-intersection requires algebraic manipulation beyond typical A-level, but follows a standard FM1 pattern. Moderately challenging for Further Maths students. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.07m Tangents and normals: gradient and equations |
6. The rectangular hyperbola $H$ has equation $x y = 25$
\begin{enumerate}[label=(\alph*)]
\item Verify that, for $t \neq 0$, the point $P \left( 5 t , \frac { 5 } { t } \right)$ is a general point on $H$.
The point $A$ on $H$ has parameter $t = \frac { 1 } { 2 }$
\item Show that the normal to $H$ at the point $A$ has equation
$$8 y - 2 x - 75 = 0$$
This normal at $A$ meets $H$ again at the point $B$.
\item Find the coordinates of $B$.\\
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\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2016 Q6 [10]}}