Geometry
Class 11-12

Hyperbola Standard Form

x2a2y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
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x²/a² - y²/b² = 1

Adjust Variables

Parameter a
a =
110
Parameter b
b =
110

Hyperbola with transverse axis 2a. Difference of distances from any point to both foci is constant (±2a).

Real-World Applications

LORAN navigation — Hyperbolic positioning using radio signal time differences.

Sonic boom — Mach cone cross-section is hyperbolic.

Nuclear cooling towers — Hyperbolic shape for structural strength.

Gear design — Hyperbolic gears for perpendicular shaft drives.

Telescope mirrors — Cassegrain telescopes use hyperbolic secondary mirrors.

Economics — Inverse demand curves (price × quantity = constant).

Physics — Special relativity: hyperbolic worldlines.

Radio astronomy — Antenna patterns have hyperbolic characteristics.

Navigation — GPS uses hyperbolic intersection of spheres.

Sundials — Hyperbolic curves for time marking.

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