# Hyperbola Calculator

Hyperbola is an open curve that has two branches that look mirror image of each other. For any point on any of the branches, the absolute difference between the point from foci is constant and equals 2a, where a is the distance of the branch from the center

## What is a Hyperbola Calculator?

'**Hyperbola Calculator**' is an online tool that helps to plot the graph of the given hyperbola equation. Online hyperbola calculator assists you to plot the hyperbola in a few seconds.

### Hyperbola Calculator

## How to Use Hyperbola Calculator?

Please follow the below steps to graph the hyperbola:

**Step 1:**Enter the given hyperbola equation in the given input box.**Step 2:**Click on the**"Compute"**button to plot the hyperbola for the given equation.**Step 3:**Click on the**"Reset"**button to clear the fields and enter the different values.

## How to Find a Hyperbola Calculator?

A hyperbola is the locus of a moving point such that the ratio of its distance from a fixed point to its distance from a fixed line is constant, i.e, it is a conic section with eccentricity e > 1

The formula of a hyperbola is :

**(x - x _{0})^{2}/(a^{2}) - (y - y_{0})^{2}/(b^{2}) = 1 (on the x-y axis)**

**Solved Example on Hyperbola Calculator:**

**Example**:

Plot the hyperbola given by the equation y^{2 }- 4x^{2} + 12x + 6y - 4 = 0 and verify it using the hyperbola calculator.

**Solution:**

The given equation can be rearranged as

(y+3)^{2} / 4 - (x-(3/2))^{2} / 1 = 1

After comparing it with the general hyperbola equation (x-x_{0})^{2}/ (a^{2}) - (y-y_{0})^{2}/ (b^{2}) = 1

Center(h, k) = (3/2,-3)

The conjugate axis will be 2b = 2

The transverse axis will be 2a = 4

And e = √(1 + (b/a)^{2}) = √(1 + (1/2)^{2}) = √5 / 2 = 1.12

The directrix will be at y + 3 = ±(a/e) = ±(2/ (√5 / 2)

y = -3 ± 4/√5

Asymptotes will be y = +(a/b)(x - h) + k and y = (-a/b)(x - h) + k

y = +(2)(x - 3/2) - 3 and y = -2(x - 3/2) -3

y = 2x - 6 and and y = -2x

The following figure shows this Hyperbola:

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