Explore Hyperbola Eccentricity

Visualize and calculate the eccentricity of a hyperbola, a key parameter defining its shape. Enter the semi-transverse axis (a) and semi-conjugate axis (b) to get started!

Hyperbola Parameters

units
units

Eccentricity Result

Eccentricity (e):
Formula: $$e = \sqrt{1 + \frac{b^2}{a^2}}$$

Hyperbola Visualization

Understanding Hyperbola Eccentricity

Eccentricity (e) is a fundamental parameter that uniquely defines the shape of a hyperbola. It's always greater than 1 for hyperbolas, indicating how much the hyperbola deviates from a parabolic shape. A larger eccentricity means a wider hyperbola.

The formula to calculate eccentricity (e) is: $$e = \sqrt{1 + \frac{b^2}{a^2}}$$, where 'a' is the semi-transverse axis (half the distance between vertices) and 'b' is the semi-conjugate axis (related to the asymptotes).

Key terms:

  • Semi-transverse Axis (a): Distance from the center to each vertex along the transverse axis.
  • Semi-conjugate Axis (b): Distance from the center to each co-vertex along the conjugate axis.

This tool helps you explore how changing 'a' and 'b' affects the eccentricity and the visual form of the hyperbola. Observe the interactive graph to see the hyperbola's shape change in real-time as you calculate different eccentricities.

Learn more about hyperbolas and eccentricity on resources like Wolfram MathWorld and Wikipedia.