Hyperbola Calculator
Calculate hyperbola properties from equation
Table of Contents
How to Use
- Select the orientation (Horizontal or Vertical)
- Enter the center coordinates (h, k)
- Enter the semi-axis lengths 'a' and 'b'
- Click Calculate to see the hyperbola properties
Hyperbola Equations
A hyperbola is the set of all points where the difference of distances from two fixed points (foci) is constant. The standard equations are:
- **Horizontal:** (x-h)²/a² - (y-k)²/b² = 1
- **Vertical:** (y-k)²/a² - (x-h)²/b² = 1
Where (h,k) is the center, 'a' is the distance from center to vertex, and 'b' relates to the conjugate axis.
Frequently Asked Questions
- What is the difference between a horizontal and vertical hyperbola?
- A horizontal hyperbola opens left and right (x-term is positive), while a vertical hyperbola opens up and down (y-term is positive).
- How do I find the foci?
- The distance 'c' from center to focus is calculated using c² = a² + b².