# ellipse

The **ellipse** is the geometric place of all points in a plane whose distances to two fixed points, called** foci**, always add up to the same constant *2a*.

d(P,F) + d(P,F’) = 2a

If C(c1,c2) is the center:

You can see that a^{2} = b^{2} + c^{2}

The** eccentricity** of an ellipse is the quotient: e = c/a. You can check that 0 < e < 1, and if c is closer to 0, the ellipse looks like a circumference.

You can draw an ellipse as follows:

You can see ellipses:

- In the trajectory of Earth in its revolution movement around the Sun.

- You can check that a line from a focus to the ellipse is reflected to the other focus. This property is used in elliptical mirrors or in Medicine, to break kidney stones through sonic waves.

**Exercise: **Calculate the equation and the eccentricity of the ellipse with center (3,-2) and whose axis measure 12 and 18.

Solution:

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