Ellipse Calculator

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

To graph an ellipse, visit the ellipse graphing calculator (choose the "Implicit" option).

Enter the information you have and skip unknown values

Enter the equation of an ellipse:
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 area:
Enter the first directrix:
Like `x=3` or `y=-5/2` or `y=2x+4`.
Enter the second directrix:
Like `x=1/2` or `y=5` or `2y-3x+5=0`.
Enter the first point on the ellipse:
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Enter the second point on the ellipse:
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For circle, see circle calculator.

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 ellipse: $$$x^{2} + 4 y^{2}=4$$$ or $$$x^{2} + 4 y^{2} - 4=0$$$.

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

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

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

Vertices: $$$\left(-2,0\right)$$$, $$$\left(2,0\right)$$$.

Co-vertices: $$$\left(0,-1\right)$$$, $$$\left(0,1\right)$$$.

Foci: $$$\left(- \sqrt{3},0\right)\approx \left(-1.73205080756888,0\right)$$$, $$$\left(\sqrt{3},0\right)\approx \left(1.73205080756888,0\right)$$$.

Focal Parameter: $$$\frac{\sqrt{3}}{3}\approx 0.577350269189626$$$.

Circumference: $$$8 E\left(\frac{3}{4}\right)\approx 9.68844822054768$$$.

Area: $$$2 \pi\approx 6.28318530717959$$$.

Eccentricity: $$$\frac{\sqrt{3}}{2}\approx 0.866025403784439$$$.

Linear eccentricity: $$$\sqrt{3}\approx 1.73205080756888$$$.

Major axis length: $$$4$$$.

Semimajor axis length: $$$2$$$.

Minor axis length: $$$2$$$.

Semiminor axis length: $$$1$$$.

First directrix: $$$x=- \frac{4 \sqrt{3}}{3}\approx -2.3094010767585$$$.

Second directrix: $$$x=\frac{4 \sqrt{3}}{3}\approx 2.3094010767585$$$.

First latus rectum: $$$x=- \sqrt{3}\approx -1.73205080756888$$$.

Second latus rectum: $$$x=\sqrt{3}\approx 1.73205080756888$$$.

The length of the latera recta: $$$1$$$.

x-intercepts: $$$\left(-2, 0\right),\left(2, 0\right)$$$.

y-intercepts: $$$\left(0, -1\right),\left(0, 1\right)$$$.

Domain: $$$\left[-2, 2\right]$$$.

Range: $$$\left[-1, 1\right]$$$.