Further Pure Mathematics WFM01: COORDINATE SYSTEMS Topical Past Paper Questions

The ellipse E has equation $$ \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 $$ The point $ P(4\cos\theta,3\sin\theta) $ lies on E where $ 0 (4) (c) Hence state the value of the maximum area for triangle OAP. (1)

The hyperbola $ H $ has equation $ \frac{x^{2}}{64} - \frac{y^{2}}{49} = 1 $ and eccentricity $ e $. (a) Show that $ e = \frac{\sqrt{113}}{8} $ (2) The point $ (8\sec\theta, 7\tan\theta) $, where $ 0 (1) The normal to H at P • has equation $8x\cos\theta + 7y\cot\theta = 113$ - me…

The plane $H_{1}$ has vector equation $$ \mathbf{r}=\left(\begin{matrix}{5}\\ {3}\\ {0}\\ \end{matrix}\right)+s\left(\begin{matrix}{3}\\ {0}\\ {1}\\ \end{matrix}\right)+t\left(\begin{matrix}{1}\\ {-2}\\ {2}\\ \end{matrix}\right) $$ where s and t are scalar parameters. (a) Determi…