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Hyperbola Definition and Equation Calculator

Online hyperbola calculator: enter the transverse and conjugate semi-axes a, b to get the focal distance, foci, eccentricity and asymptotes.

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x²/a²−y²/b²=1, c²=a²+b²
Positive
Conjugate

📖 Tutorial | Hyperbola

1. Definition
Points whose absolute difference of distances to F₁, F₂ is 2a form a hyperbola, equation x²/a²−y²/b²=1.
2. Formula & Notation
a,bSemi-axes
3. Properties & Laws
  • Foci (±c,0);
  • c²=a²+b²;
  • Asymptotes y=±(b/a)x;
  • e>1.
4. Steps
  1. Enter a,b>0;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: 3,4: c=5, e=5/3, asymptotes y=±4/3 x.
6. Common Pitfalls
Plus sign in c²;
Slope b/a;
e>1.

❓ FAQ | Hyperbola

Definition?
Difference 2a.
c?
a²+b².
Asymptotes?
b/a.
e?
>1.
Rectangular?
√2.
Foci on y?
y² first.
Ellipse?
Different signs.