| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parametric point verification |
| Difficulty | Moderate -0.8 This is a straightforward question on rectangular hyperbolas requiring only basic manipulation: (a) eliminate parameter by multiplying x and y to get xy=25 (1 mark of pure algebra), and (b) substitute t-values to find coordinates then use midpoint formula (3 marks of routine calculation). No problem-solving or geometric insight needed, just direct application of standard techniques. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian |
The rectangular hyperbola, $H$, has parametric equations $x = 5t, y = \frac{5}{t}, t \neq 0$.
\begin{enumerate}[label=(\alph*)]
\item Write the cartesian equation of $H$ in the form $xy = c^2$.
[1]
\item Points $A$ and $B$ on the hyperbola have parameters $t = 1$ and $t = 5$ respectively.
Find the coordinates of the mid-point of $AB$.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q3 [4]}}