| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Find intersection points |
| Difficulty | Standard +0.3 This is a straightforward parametric intersection problem requiring substitution of parametric equations into a linear equation, solving the resulting quadratic, and finding coordinates. While it involves multiple steps and algebraic manipulation, the techniques are standard for Further Maths students with no novel insight required, making it slightly easier than average. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03g Parametric equations: of curves and conversion to cartesian |
4. The rectangular hyperbola $H$ has parametric equations
$$x = 4 t , \quad y = \frac { 4 } { t }$$
The straight line with equation $3 y - 2 x = 10$ intersects $H$ at the points $A$ and $B$.
Given that the point $A$ is above the $x$-axis,
\begin{enumerate}[label=(\alph*)]
\item find the coordinates of the point $A$ and the coordinates of the point $B$.
\item Find the coordinates of the midpoint of $A B$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2017 Q4 [7]}}