the foci (2 focal points) and the distance between the vertices.
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The two foci are necessary to define the location of an ellipse, but the shape depends on the eccentricity, which is related to the lengths of the two axes.
guadrilateral
The width reduces as the length increases. The changes shape of the curve is a part of a [rectangular] hyperbola.
change of position, shape, or size of figure
if you multiply all the points by one you get the same points so the shape stays the same.