Hyperbola Calculator
Enter values to calculate hyperbola properties.
Standard Forms of Hyperbola Equations
Horizontal Hyperbola
\[ \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1 \]
Vertical Hyperbola
\[ \frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1 \]
Step-by-Step Hyperbola Calculations
Example 1: Finding Foci
Given: \[ \frac{x^2}{16} - \frac{y^2}{9} = 1 \]
- Identify \(a^2 = 16 \Rightarrow a = 4\)
- Calculate \(c = \sqrt{a^2 + b^2} = \sqrt{16 + 9} = 5\)
- Foci at \((\pm5, 0)\)
Advanced Hyperbola Concepts
Eccentricity Formula
\[ e = \frac{c}{a} \]
- Always \(e > 1\) for hyperbolas
- Measures "openness" of hyperbola
