An ellipse is a stretched circle. Slice a cone at a slant and an ellipse falls out. Planets orbit on ellipses, racetracks are roughly elliptical, and whisper galleries are ellipsoidal rooms where a quiet word at one focus carries to the other.
Equation
x²/a² + y²/b² = 1
a = semi-major axis (long), b = semi-minor axis (short)
Two-foci property
PF₁ + PF₂ = 2a
Sum of distances from any point P to the two foci is constant — equals the long axis length.
Kepler's first law: every planet moves in an ellipse with the Sun at one focus. The other focus is just an empty point in space.