AS/A2 Pure 4 Pure 6

P5 Topic 1: Coordinate Systems
The conic curves
Use your mouse to move the five points about. A graph through these points is displayed. What kinds of graphs can you get? Can you get any of the conic curves - the circle, ellipse, parabola or hyperbola?

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

Summary to begin with, the curve is an ellipse by adjusting the points slightly you can make a circle if one point is moved within the quadrilateral formed by the other four, then a hyperbola is displayed in the last case, by adjusting the points sloght you can make a rectangular hyperbola a parabola is not so easy to display. Try moving the points to these coordindates: (0,0), (1,1), (-1,1), (2,4) and (-2,4). The curve disdplayed will be the parabola y = x2 Uses Cinderella interactive geometry.