| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2020 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola area calculations |
| Difficulty | Standard +0.8 This is a multi-part Further Maths question requiring: (a) finding parameter a by using tangency conditions with implicit differentiation or parametric forms, (b) finding the point of tangency, and (c) calculating a triangle area involving the focus and directrix. While it tests standard parabola theory from F1, it requires coordinating multiple concepts (tangency, focus-directrix properties, coordinate geometry) across three connected parts, making it moderately challenging but still within standard Further Maths expectations. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.07m Tangents and normals: gradient and equations |
| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |
7. The parabola $C$ has equation $y ^ { 2 } = 4 a x$, where $a$ is a positive constant.
The line $l$ with equation $3 x - 4 y + 48 = 0$ is a tangent to $C$ at the point $P$.
\begin{enumerate}[label=(\alph*)]
\item Show that $a = 9$
\item Hence determine the coordinates of $P$.
Given that the point $S$ is the focus of $C$ and that the line $l$ crosses the directrix of $C$ at the point $A$,
\item determine the exact area of triangle $P S A$.\\
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VIXV SIHIANI III IM IONOO & VIAV SIHI NI JYHAM ION OO & VI4V SIHI NI JLIYM ION OO \\
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\hfill \mbox{\textit{Edexcel F1 2020 Q7 [10]}}