Hyperbola Calculator

This calculator will find either the equation of the hyperbola (standard form) from the given parameters or the center, vertices, co-vertices, foci, asymptotes, focal parameter, eccentricity, linear eccentricity, latus rectum, length of the latus rectum, directrices, (semi)major axis length, (semi)minor axis length, x-intercepts, and y-intercepts of the entered hyperbola.

To graph a hyperbola, visit the hyperbola graphing calculator (choose the "Implicit" option).

Enter the information you have and skip unknown values

Enter the equation of a hyperbola:
In any form you want: `x^2-4y^2=1`, `-x^2/9+y^2/16=1`, etc.
Enter the center:
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Enter the first focus:
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Enter the second focus:
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Enter the first vertex:
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Enter the second vertex:
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Enter the first co-vertex:
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Enter the second co-vertex:
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Enter the eccentricity:
Enter the major axis length:
Enter the semimajor axis length:
Enter the minor axis length:
Enter the semiminor axis length:
Enter the first asymptote:
Like `y=-(4x)/3+2` or `x-5y+7=0`.
Enter the second asymptote:
Like `y=4x-1` or `y-2x=5`.
Enter the first directrix:
Like `x=-7/3` or `y=5/4` or `2y-x=4`.
Enter the second directrix:
Like `x=5` or `y=-2/7` or `y-x/2+7/4=0`.
Enter the first point on the hyperbola:
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Enter the second point on the hyperbola:
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If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

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