Hyperbola Asymptote Calculator
Vertices, foci and asymptotes of a hyperbola.
Enter your values
Enter the a you are working with.
Enter the b you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Foci
- (±5, 0)
- Vertices
- (±4, 0)
- Asymptotes
- y = ±0.75x
- Eccentricity
- 1.25
Quick answer
For x^2/a^2 - y^2/b^2 = 1, the asymptotes are y = ±(b/a)x and c = sqrt(a^2+b^2).
c = sqrt(a^2+b^2), asymptotes y=±(b/a)x
At a glance
| What it does | Vertices, foci and asymptotes of a hyperbola. |
|---|---|
| Category | Math |
| Inputs needed | a, b |
| Main output | Foci |
| Formula | c = sqrt(a^2+b^2), asymptotes y=±(b/a)x |
| Cost | Free — no sign-up, no download |
How to use the Hyperbola Asymptote Calculator
- 1Enter a (distance to vertex) and b (conjugate semi-axis).
- 2Read off vertices, foci and eccentricity.
- 3Use the asymptote slope ±b/a to sketch the hyperbola's guide lines.
Inputs explained
- a
- Enter the a you are working with.
- b
- Enter the b you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- a4
- b3
Results
- Foci(±5, 0)
- Vertices(±4, 0)
- Asymptotesy = ±0.75x
- Eccentricity1.25
Frequently asked questions
What if the hyperbola opens vertically?
Swap the roles of x and y — asymptotes become y = ±(a/b)x.
Is eccentricity always > 1?
Yes, for any hyperbola e > 1.
What do I need to enter into the Hyperbola Asymptote Calculator?
Just 2 values: a, b. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Hyperbola Asymptote Calculator work out the answer?
For x^2/a^2 - y^2/b^2 = 1, the asymptotes are y = ±(b/a)x and c = sqrt(a^2+b^2). It applies the formula c = sqrt(a^2+b^2), asymptotes y=±(b/a)x and shows the working so you can check each step by hand.
Is the Hyperbola Asymptote Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.