Hyperbola Properties
Foci, vertices, and asymptotes of a hyperbola
About this calculator
The Hyperbola Properties Calculator takes a hyperbola in standard form — semi-transverse axis a, semi-conjugate axis b, center (h, k), and orientation — and reports the focal distance c = √(a² + b²), the eccentricity c/a, the vertices, co-vertices, and foci, the asymptote slopes, the latus rectum 2b²/a, and the distance from the center to each directrix. Both a and b must be positive.
How to use the Hyperbola Properties calculator
- Enter the measurements you know into the input fields.
- Read the computed properties — they update instantly as you type.
- Compare the diagram with your figure to confirm the setup is right.
- Copy the page URL to share the exact calculation.
Common examples
- a = 3, b = 4, horizontal, centered at origin → c = 5, eccentricity ≈ 1.667, foci (±5, 0)
- a = 5, b = 12, vertical, center (2, −1) → c = 13, e = 2.6, foci (2, −14) and (2, 12)
- a = 1, b = 1 → rectangular hyperbola: asymptote slopes ±1, e = √2 ≈ 1.4142
- a = 3, b = 4 → latus rectum ≈ 10.6667, directrices at offset 1.8 from the center
Frequently asked questions
How does the Hyperbola Properties calculator work?
Enter the known measurements of your figure and the calculator applies the standard geometric formulas to find the remaining properties, alongside a diagram that reflects your numbers. All values are computed with high-precision arithmetic.
When would I use the Hyperbola Properties calculator?
It helps with geometry homework, technical drawing, construction and DIY layout, and any situation where you know some measurements of a shape and need the rest.
How accurate are the results?
Formulas are evaluated at 30 significant digits of precision internally, including roots and trigonometric functions. Displayed values are rounded for readability, but the underlying computation does not accumulate floating-point drift.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same figure and results for whoever clicks it.