| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Rectangular hyperbola normal re-intersection |
| Difficulty | Standard +0.3 This is a standard Further Pure 1 rectangular hyperbola question with routine parametric form verification, normal equation derivation using standard formulas, and solving a quadratic to find re-intersection. All steps follow textbook procedures with no novel insight required, making it slightly easier than average for Further Maths. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
| VIAV SIHI NI BIIIM ION OC | VGHV SIHI NI GHIYM ION OC | VJ4V SIHI NI JIIYM ION OC |
\begin{enumerate}
\item The rectangular hyperbola $H$ has equation $x y = 25$\\
(a) Verify that, for $t \neq 0$, the point $P \left( 5 t , \frac { 5 } { t } \right)$ is a general point on $H$.
\end{enumerate}
The point $A$ on $H$ has parameter $t = \frac { 1 } { 2 }$\\
(b) 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 $B$.\\
(c) Find the coordinates of $B$.\\
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VIAV SIHI NI BIIIM ION OC & VGHV SIHI NI GHIYM ION OC & VJ4V SIHI NI JIIYM ION OC \\
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\hfill \mbox{\textit{Edexcel F1 2018 Q6 [10]}}