Unit 11
Conic sections.
Circle, ellipse, parabola and hyperbola as slices of a cone: eccentricity, the foci, and Dandelin spheres.
Before this unit
The unit, lesson by lesson
Lessons
3 lessons · 16 practice questions · about an hour
Slicing a cone
Four curves from one cut: circle, ellipse, parabola and hyperbola, set by the cut’s tilt against the cone’s side, the radius of a level cut, why the distance from the tip changes only the size, and what happens in a cut through the tip.
Eccentricity
One number for a conic section’s shape: the eccentricity e, from 0 for a circle to more than 1 for a hyperbola, how to work it out from the tilt, why size does not change it, and its link to the foci, e = c/a.
Foci and Dandelin spheres
Why an ellipse has two foci whose distances add up to a constant: Dandelin spheres, the gardener’s ellipse with a string, the link between a, b and c, the parabola with one focus and a directrix, and the hyperbola with a fixed difference.