The parabolaEdexcel International A Level Further Maths: Mind map

Exam questions on The parabola

1. The parabola $C$ has equation $y^2=12x$. Its focus is $S$.
   The point $P(12,12)$ lies on $C$. Use the focus-directrix property to find the distance $SP$.2 marks
2. The parabola $C$ has equation $y^2=8x$. A general point on $C$ has coordinates $(2t^2,4t)$, where $t$ is a parameter.
   The point $Q(50,-20)$ lies on $C$. Find the value of $t$ at $Q$.2 marks
3. The parabola $C$ has equation $y^2=16x$, focus $S$ and directrix $l$. The point $P(4t^2,8t)$ lies on $C$.
   Show that the distance $SP$ is equal to the perpendicular distance from $P$ to the directrix.3 marks