The ellipse and hyperbolaEdexcel International A Level Further Maths: Mind map

Exam questions on The ellipse and hyperbola

1. The ellipse $E$ has parametric equations $x=5\cos t$, $y=3\sin t$, for $0\le t<2\pi$.
   Find the value of $t$, for $0\le t<2\pi$, at the point $\left(4,-\frac95\right)$ on $E$. Give your answer to 3 significant figures.2 marks
2. The hyperbola $H$ has Cartesian equation $\frac{x^2}{9}-\frac{y^2}{16}=1$.
   Show that $x=3\cosh t$, $y=4\sinh t$ satisfies the Cartesian equation of $H$.2 marks
3. The ellipse $E$ has Cartesian equation $\frac{x^2}{16}+\frac{y^2}{4}=1$.
   Write down parametric equations for $E$. Hence find the exact value of the parameter $t$, for $0<t<\frac{\pi}{2}$, at the point $\left(2\sqrt2,\sqrt2\right)$ on $E$.3 marks