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Hyperbola Calculator

Hyperbola Calculator

Provide all necessary parameters of the hyperbola equation and the calculator will instantly find the center, eccentricity, focal parameter, and angle, with the steps shown.


Hyperbola Equation

\[\frac{(x-x_0)^2}{a} - \frac{(y-y_0)^2}{b} = 1\]

Enter the Center(C)(x0, y0):

Enter x0:

Enter y0:

Enter a:

Enter b:

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An online hyperbola calculator will help you to determine the center, eccentricity, focal parameter, major, and asymptote for given values in the hyperbola equation. Also, this calculator precisely finds the covertices and conjugate of a function. In this context, you can understand how to find a hyperbola, it’s a graph and the standard form of hyperbola.

What is Hyperbola?

In mathematics, a hyperbola is one of the conic section types formed by the intersection of a double cone and a plane. In a hyperbola, the plane cuts off the two halves of the double cone but does not pass through the apex of the cone. The other two cones are parabolic and elliptical. In other words, a hyperbola is a set of all points on the planes, for which the absolute value of the difference between the distances and two fixed points (known as foci of hyperbola) is constant.

hyperbola calculator

Hyperbola Formula:

A hyperbola at the origin, with x-intercepts, points a and – a has an equation of the form

$$ X^2 / a^2 – y^2 / b^2 =1 $$

While a hyperbola centered at an origin, with the y-intercepts b and -b, has a formula of the form

$$ y^2 / b^2 – x^2 / a^2 = 1 $$

Some texts use \( y^2 / a^2 – x^2 / b^2 = 1 \) for this last equation. For a brief introduction such as this, the form given is commonly used.

The x-intercepts are the vertices of the hyperbola with the formula \( x^2 / a^2 – y^2 / b^2 = 1 \), and the y-intercepts are the vertices of a hyperbola with the formula \( y^2 / b^2 – x^2 / a^2 = 1\). The line between the midpoint of the transverse axis is the center of the hyperbola and the vertices are the transverse axis of the hyperbola.


Graph the hyperbola. Find its vertices, center, foci, and the equations of its asymptote lines.

$$ a^2/ 16 – b^2 / 25 = 1 $$

A hyperbola with center point at (0, 0), and its changed axis is along the x‐axis.

$$ M^2 = 16, n^2 = 25 $$

$$ k = \sqrt {a^2 + b^2} $$

$$ |a| = 4, |b| = 5 $$

$$ = \sqrt {16 + 25} $$

If you are facing some issues about foci, vertices and coordinates then use our hyperbola calculator that can find all attributes using the equation of a hyperbola quickly.

Vertices: (–4, 0) (4, 0)

Foci: \( (- \sqrt{41}, 0) ( \sqrt{41}, 0) \)

Equations of asymptote lines: b = 5/4 a

A hyperbola centered at (0, 0) whose axis is along the y‐axis has the following formula as hyperbola standard form.

$$ y^2 / m^2 – x^2 / b^2 = 1 $$

The vertices are (0, – x) and (0, x). The foci are at (0, – y) and (0, y) with \( z^2 = x^2 + y^2 \) . The asymptote lines have formulas a = x / y b

In general, when the hyperbola is written in the standard format, the axis in the hyperbola graph is parallel or along to the axis of a variable that is not being subtracted.

Hyperbola Calculator vertex and focus

How Hyperbola Calculator Works?

The hyperbola equation calculator will compute the hyperbola center using its equation by following these guidelines:


  • Firstly, the calculator displays an equation of hyperbola on the top.
  • Now, substitute the values for different points according to the hyperbola formula.
  • Click on the calculate button for further process.


  • The hyperbola calculator provides the equation with input values.
  • The calculator displays the results for the center, vertices, eccentricity, parameter, asymptote, directrix, latus rectum, x, and y-intercepts precisely.


Is a parabola half of a hyperbola?

A pair of hyperbolas formed by the intersection of the plane with two equal cones on the opposite sides of the same vertex. Therefore, this assumes that each half of the parabola that we usually think of is itself a hyperbola. A hyperbola is just a continuous curve similar to a parabola.

What is the parabola in real life?

When the liquid rotates, the gravity forces turn the liquid into a parabolic shape. The most common real-life example is when you stir up lemon juice in a glass or jug by rotating it around its axis.

Is Eiffel Tower a hyperbola?

No, the Eiffel Tower is not an example of hyperbola. It is known to take the form of a parabola.

Is the guitar a hyperbola?

A guitar is a real example of hyperbola because of its different sides and how it’s curved going outwards like a hyperbola. This is an important example for the real world because people who studying to play the guitar and understand it more simply because of its hyperbolic shape.

Why is the hourglass a hyperbola?

The hourglass creates a hyperbola in which two cones meet. The sides of the hourglass make an imaginary hyperbola. The purpose of this structure is to make the sand particle only comes through the center point. This will help to control the sand to keep it stable for 1 hour or a minute.

How useful is the concept of hyperbola in radar tracking stations?

Focus on one “point”. This hyperbola property is used for radar tracking stations: detecting an object by sending sound waves in a different direction from two Point sources: The concentric circles of these sound waves intersect the hyperbola.


Use this online hyperbola calculator for the standard hyperbola equation for the given parameters or obtaining the axis length and the coordinates for the given input values in an equation for hyperbola.


From the source of Wikipedia: As the locus of points, Hyperbola with equation, By the directrix property, Construction of a directrix, Pin and string construction, Steiner generation of a hyperbola.

From the source of Lumen: hyperbola centered at the origin, axes of symmetry, transverse axis, the center of a hyperbola, central rectangle, Equation of a Hyperbola Centered at the Origin.

From the source of Purple Math: hyperbola is centered on a point, Inscribed angles for hyperbolas, parametric representation, implicit representation, hyperbola in space, Tangent construction, Area of the grey parallelogram, Point construction.