The eccentricity of the ellipse is the measure of how much the conic section deviates from being circular.

The eccentricity of a conic is .

Here  is the distance between center and the focus.

 is the distance between focus to a vertex.

For an ellipse :  then .

Eccentricity of the ellipse .

Change in the eccentricity will change the distance between center and focus.

More the eccentricity, more will be the distance between center and focus.

Hence the ellipse will be elongated and less circular.

Less the eccentricity, less will be the distance between center and focus.

Hence the ellipse will be more circular.

Eccentricity of the ellipse .

More the eccentricity, the ellipse will be elongated and less circular.

Less the eccentricity, the ellipse will be more circular.