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What Is Hyperbola?

Whether you are in high school or college, the hyperbola equation calculator is an innovative tool that you cannot afford to ignore. We journey through the features and benefits you can get out of this calculator.


The hyperbola is an open curve lying in a plane, consisting of two equal cones symmetrical to the same vertex. It has two pieces, namely, connected components or branches. These two are mirror images of each other, and they resemble two infinite bows.

There are various forms of the hyperbola calculator:

Hyperbola Standard Form Calculator

The standard form of a hyperbola is that which is written in such a way so that you can see useful information by just looking at the numbers. Therefore, the standard form of a hyperbola opening sideways is (x - h) ^2 / a^2 - (y - k) ^2 / b^2 = 1.

When you have one that opens up and down, its standard form is (y - k) ^2 / a^2 - (x - h) ^2 / b^2 = 1. For the hyperbola that opens sideways, you will note that the x appears first, while for one that opens up and down, the y appears first.

  • Graph Hyperbola Calculator

A mix of two parabolas forms a graph — each being a perfect mirror image of the other. They also open away from one another.

  • Hyperbola Asymptote Calculator

The asymptote of hyperbola refers to the lines that pass through the hyperbola center, intersecting a rectangle's vertices with side lengths of 2a and 2b. The hyperbola asymptotes' equations are y=k± b a (x−h) and y=k± a b (x−h). 

  • The Foci of Hyperbola

These are the two fixed points of the hyperbola. 

The Equation of Hyperbola Calculator

When you want to find equation of hyperbola calculator, you should have the following:

  • Center coordinates (h, k)

a = distance from vertices to the center

c = distance from foci to center

Therefore, you will have the equation of the standard form of hyperbola calculator as:

  • c 2 = a 2 + b 2 ∴b= c 2 − a 2

When the transverse axis is horizontal, the equation of the hyperbola graph calculator will be:

  • ( x−h ) 2 a 2 − ( y−k ) 2 b 2 =1 

Whereas when the transverse axis is vertical, the equation becomes:

  • (y−k) 2 a 2 − (x−h) 2 b 2 =1 

Using The Hyperbola Calculator

To find equation of hyperbola given foci and vertices using this calculator:

  • Insert the relevant values into the function tab
  • Click on 'Calculate'
  • Find your answer in a new window

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