| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | June |
| 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, implicit differentiation for the normal, and solving a quadratic. All techniques are standard with no novel insight required, making it slightly easier than average for F1. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.03g Parametric equations: of curves and conversion to cartesian1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07m Tangents and normals: gradient and equations |
8. The hyperbola $H$ has cartesian equation $x y = 16$
The parabola $P$ has parametric equations $x = 8 t ^ { 2 } , y = 16 t$.
\begin{enumerate}[label=(\alph*)]
\item Find, using algebra, the coordinates of the point $A$ where $H$ meets $P$.
Another point $B ( 8,2 )$ lies on the hyperbola $H$.
\item Find the equation of the normal to $H$ at the point (8, 2), giving your answer in the form $y = m x + c$, where $m$ and $c$ are constants.
\item Find the coordinates of the points where this normal at $B$ meets the parabola $P$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2014 Q8 [14]}}