| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2021 |
| Session | November |
| Marks | 3 |
| Topic | Polar coordinates |
| Type | Show polar curve has Cartesian form |
| Difficulty | Standard +0.3 This is a straightforward polar-to-Cartesian conversion requiring standard substitutions (r² = x² + y², x = r cos θ, sec θ = 1/cos θ = r/x) and algebraic manipulation. The working is routine with clear steps and no conceptual difficulty beyond applying memorized formulas, making it slightly easier than average. |
| Spec | 4.09a Polar coordinates: convert to/from cartesian |
The equation of a curve in polar coordinates is
$$r = 11 + 9 \sec \theta.$$
Show that a cartesian equation of the curve is
$$(x - 9)\sqrt{x^2 + y^2} = 11x.$$
[3 marks]
\hfill \mbox{\textit{SPS SPS FM 2021 Q2 [3]}}