In the past, I’ve had my students do a memory aid for all of the conics, uploaded to their blogs. This year, you will be making a memory aid, but using geogebra. Since that’s probably more work, I’ve decided that you don’t have to do all the conics – you can make it about the ellipse OR the parabola. I’ve already done the hyperbola for you, so that one’s off the table. But you can use it as a guide so you can get an idea of what I’m looking for.
Your geogebra must include:
- the graph of the conic (see the dark blue and dark green on the hyperbola ggb)
- a display of the rule(s) of the conic, showing the parameters involved in the rule
- sliders for those parameters that change the graph of the conic accordingly
- the values allowed by the sliders should make sense for the conic
- both orientations of the conic (vertical and horizontal)
- for the ellipse: points indicating the foci, the vertices, and their coordinates, segments indicating the major and minor axes, and their lengths
- for the parabolas: points indicating the vertex, the focus, and their coordinates, a line indicating the directrix, and its rule
- a point P that can be moved anywhere on the conic by selecting and dragging it (ie you don’t need a formula for it)
- for the ellipse, the focal radii for the point P, wherever it is, labelled L1 and L2
- the string property displayed as the point P moves around/along the conic (see the light blue and light green on the hyperbola.)
- show the strings and their lengths
- for the ellipse show the L1 + L2 property
- for the parabola show the L1 = L2 property