Hyperbola calculator

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.

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-x0)2/ (a2) - (y-y0)2/ (b2) = 1   (on the x-y axis)

 

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Solved Example:

Example: Plot the hyperbola given by the equation y− 4x2 + 12x + 6y − 4 = 0

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-x0)2/ (a2) - (y-y0)2/ (b2) = 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:

Sours: https://www.cuemath.com/calculators/hyperbola-calculator/

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Hyperbola Calculator

Answer

Equation of the hyperbola: $$$x^{2} - 4 y^{2}=49$$$ or $$$x^{2} - 4 y^{2} - 49=0$$$.

Graph: to graph the hyperbola, visit the hyperbola graphing calculator (choose the "Implicit" option).

Standard form: $$$\frac{x^{2}}{49} - \frac{4 y^{2}}{49}=1$$$.

Center: $$$\left(0,0\right)$$$.

Vertices: $$$\left(-7,0\right)$$$, $$$\left(7,0\right)$$$.

Co-vertices: $$$\left(0,- \frac{7}{2}\right)$$$, $$$\left(0,\frac{7}{2}\right)$$$.

Foci: $$$\left(- \frac{7 \sqrt{5}}{2},0\right)\approx \left(-7.82623792124926,0\right)$$$, $$$\left(\frac{7 \sqrt{5}}{2},0\right)\approx \left(7.82623792124926,0\right)$$$.

Eccentricity: $$$\frac{\sqrt{5}}{2}\approx 1.11803398874989$$$.

Linear eccentricity: $$$\frac{7 \sqrt{5}}{2}\approx 7.82623792124926$$$.

Focal Parameter: $$$\frac{7 \sqrt{5}}{10}\approx 1.56524758424985$$$.

Major (transverse) axis length: $$$14$$$.

Semimajor axis length: $$$7$$$.

Minor (conjugate) axis length: $$$7$$$.

Semiminor axis length: $$$\frac{7}{2}$$$.

First asymptote: $$$y=- \frac{x}{2}$$$

Second asymptote: $$$y=\frac{x}{2}$$$

First directrix: $$$x=- \frac{14 \sqrt{5}}{5}\approx -6.26099033699941$$$.

Second directrix: $$$x=\frac{14 \sqrt{5}}{5}\approx 6.26099033699941$$$.

First latus rectum: $$$x=- \frac{7 \sqrt{5}}{2}\approx -7.82623792124926$$$.

Second latus rectum: $$$x=\frac{7 \sqrt{5}}{2}\approx 7.82623792124926$$$.

The length of the latera recta: $$$\frac{7}{2}$$$.

x-intercept: $$$\left(0, 0\right)$$$.

y-intercept: $$$\left(0, 0\right)$$$.

Sours: https://www.emathhelp.net/calculators/algebra-2/hyperbola-calculator/

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Calculator hyperbola

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