AS/A2 Pure 4 Pure 6

P5 Topic 1: Coordinate Systems
The parabola
Use your mouse to move point X left or right. How does point Z move? How does its position relate to the position of point O and the red line? Now move point O or use points A and B to move the red line. What can you say now about the position of Z?

Please enable Java for an interactive construction (with Cinderella).

Summary the orange curve is a parabola the point Z is always the same distance from O as it is from the red line the point O is called the focus the red line is called the directrix Typically, a parabola has equation y2 = 4ax and has its focus at (a,0) and directrix at x = -a. Uses Cinderella interactive geometry.