| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Rectangular hyperbola normal equation |
| Difficulty | Standard +0.3 This is a straightforward calculus application requiring implicit differentiation to find the gradient, then using point-normal form. The parametric form is given, making it a routine 5-mark question with clear steps: differentiate, find gradient at P, find perpendicular gradient, substitute into line equation. Slightly easier than average due to being a 'show that' with the answer provided. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
Show that the normal to the rectangular hyperbola $xy = c^2$, at the point $P \left( ct, \frac{c}{t} \right)$, $t \neq 0$ has equation
$$y = t^2 x + \frac{c}{t} - ct^3.$$
[5]
\hfill \mbox{\textit{Edexcel FP1 Q20 [5]}}