Geometry
Class 11-12

Ellipse Standard Form

x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
−4−202400.511.522.53
x²/a² + y²/b² = 1

Adjust Variables

Semi-major a
a =
110
Semi-minor b
b =
110

Ellipse with semi-major axis a and semi-minor axis b. Sum of distances from any point to both foci is constant (2a).

Real-World Applications

Planetary orbits — All planets orbit the Sun in ellipses (Kepler's first law).

Whispering galleries — Elliptical rooms focus sound between foci.

Medical imaging — Elliptical CT scanner gantries.

Gear design — Elliptical gears for variable speed ratios.

Architecture — Elliptical arches and domes.

Sports tracks — Running track shape (two semicircles + straight sections).

Pool tables — Elliptical table sends ball through both foci.

Astronomy — Cometary orbits are highly elliptical.

Optics — Ellipsoidal mirrors in telescopes.

Mapmaking — Ellipsoidal Earth model for GPS.

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