Further Mathematics/Coordinate geometry instrument 08

01/ 08

Conic-section rig

Rotate the double cone

Inspect one surface from every side.

Drag anywhere on the model. The two nappes meet at one vertex.

As the plane approaches parallel to a generator, what happens to the second sphere?

Teacher cue

Ask: What remains unchanged as we rotate the view?
Look for: The cone itself; only our viewpoint changes.
Then: Insert a cutting plane.

Plane tilt 28.0° horizontalthrough both nappes Model zoom 100% 70%190%

Section specimen Fixed view

Scene layers2 shown

Visible on model

Choose visible scene layers Scene objects Cone body Cutting plane Section curve Dandelin spheres Focus points AaModel labels Focal proof segments PF₁ PA PF₂ PB AB fixed span

Keyboard: left and right arrows change step, space controls motion, R resets. Drag the model to rotate it.