Ellipse and hyperbolaEdexcel A-Level Further Maths: Mind map

Exam questions on Ellipse and hyperbola

1. The ellipse $E$ has equation $\frac{x^2}{25}+\frac{y^2}{16}=1$.
   The point $P$ on $E$ has $x$-coordinate $\frac{10}{3}$. Use the focus-directrix property to find the distance from $P$ to the focus $(3,0)$.2 marks
2. The hyperbola $H$ has equation $\frac{x^2}{9}-\frac{y^2}{16}=1$, with parametric equations $x=3\sec t$, $y=4\tan t$.
   Find the exact gradient of $H$ at the point $P\left(6,4\sqrt3\right)$.2 marks
3. The hyperbola $H$ has equation $\frac{x^2}{4}-\frac{y^2}{9}=1$, with parametric equations $x=2\sec t$, $y=3\tan t$.
   The line $y=2x+k$ is a tangent to $H$. Find the possible values of $k$.3 marks