Ellipse calculator

Ellipse Calculator is an online math tool that shows how to find the center, minor and major axes, eccentricity, focus and vertices. The calculator shows all steps on how to find unknown ellipse parameters.

Ellipse calculator

find center, axes, eccentricity, focus, vertices ...
help ↓↓ examples ↓↓

Ellipse equation is in

$x^2$

$+$

$y^2$

$=$

$1$

$(x$

$)^2$

$+$

$(y$

$)^2$

$=$

$1$

$x^2$

$+$

$y^2$

$=$

To enter square roots, type r $ \left( \color{blue}{\text{ r18 } = \sqrt{18}} ~ \right) $.

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Ellipse formulas

$$ c = \sqrt{a^2 - b^2} $$

Linear Eccentricity

$$ e = \dfrac{c}{a} $$

Eccentricity

$$ F_1\left(c,0\right) ~~ , ~~ F_2\left(-c,0\right) $$

Foci

$$ V_1\left(a,0\right) ~~ , ~~ V_2\left(-a,0\right) $$

Vertices

$$C_1\left(0,a\right) ~~ , ~~ C_2\left(0,-a\right) $$

Co-vertices

examples

example 1:ex 1:

Determine the coordinates of the foci of the ellipse $$ \frac{x^2}{9} + \frac{y^2}{16} = 1 $$

example 2:ex 2:

Find the coordinates of the foci of the ellipse given by $$ \frac{4(x-3)^2}{12} + \frac{8(y+6)^2}{20} = 1 $$

example 3:ex 2:

Find the major axis of the ellipse given by $$ 4x^2 + 9y^2 = 36 $$

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