A circle is perfectly round, and has one center. An ellipse is like a circle with TWO "centers", and each "center" is called a "focus". The plural of "focus" is "foci".
Take a piece of string and tie a loop in each end. Put a pin through the loops, and hold it still in the center of the circle. Place the tip of your pencil at the center of the string, and you can draw a circle by keeping the string taut.
Now take TWO pins, and put one pin at each end of the string; place the pins at some short distance apart, and hold them there. Place your pencil and draw, and the shape you draw will be an ellipse. The two pinpoints are the focuses, or foci, of the ellipse.
Eccentricity is a measure of how far the ellipse varies from a circle. An ellipse with an eccentricity of zero _IS_ a circle, while an eccentricity of 1.0 is a straight line, with that string stretched out straight.
In astronomy, every natural orbit is an ellipse.
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The two fixed points are the foci but these do not define the shape of the ellipse. You also need to know the eccentricity.
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An ellipse is very eccentric when its foci are far apart.The closer one focus is to the other, the less eccentric the ellipse is.When when both foci are the same point, the eccentricity is zero, and the ellipse is a circle.
If the eccentricity was 0 the ellipse would instead be a circle, and if the eccentricity was 1 it would be a straight line segment.