From Circle to Needle

Eccentricity e measures how stretched an ellipse is. Keep a fixed and vary e = c/a.

Teaching Notes

Core Idea

Eccentricity controls conic shape while preserving the reflection property for ellipses.

Try This

At e=0, compare to a circle. Then move to e=0.9 and describe how the focal points move.

Teacher Prompt

“If e increases, which of a, b, c changes most visibly on-screen?”

Vocabulary

  • Eccentricity: stretch parameter, e=c/a.
  • Circle: special ellipse with e=0.
  • Elongated ellipse: e close to 1.