Hyperbola Calculator
Compute vertices, foci, and asymptotes of a hyperbola.
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Introduction
Hyperbola Calculator — Compute vertices, foci, and asymptotes of a hyperbola. Enter a, b to get an instant, accurate result.
Formula
For x²/a² − y²/b² = 1: vertices are at (±a, 0), foci are at (±c, 0) where c = √(a²+b²), and the asymptotes have slope ±b/a.
Step-by-step
- Enter the a.
- Enter the b.
- Click Calculate to see your result instantly.
Real-world example
Example: With a = 3, b = 4, the Hyperbola Calculator gives Vertices: 3, -3, Foci: 5, -5, Asymptote Slope: 1.3333.
Frequently Asked Questions
How do the asymptotes relate to the hyperbola?
The two branches of the hyperbola approach, but never touch, these two straight lines as they extend outward.
Why is c larger than a here?
Unlike an ellipse, a hyperbola's foci distance c = √(a²+b²) is always greater than a.
What inputs does the Hyperbola Calculator need?
You'll need to provide: a, b. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Hyperbola Calculator?
The Hyperbola Calculator applies the formula exactly as calculated — For x²/a² − y²/b² = 1: vertices are at (±a, 0), foci are at (±c, 0) where c = √(a²+b²), and the asymptotes have slope ±b/a. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Hyperbola Calculator free to use?
Yes, the Hyperbola Calculator is completely free, requires no signup, and runs instantly in your browser.
About the Hyperbola Calculator
The Hyperbola Calculator uses a real, verifiable formula — For x²/a² − y²/b² = 1: vertices are at (±a, 0), foci are at (±c, 0) where c = √(a²+b²), and the asymptotes have slope ±b/a. — so results are accurate every time, not an approximation.