Ellipse - Special Cases of an Ellipse

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In the equation c2 = a2 – b2 obtained above, if we keep a fixed and vary c from 0 to a, the resulting ellipses will vary in shape.
Case (i): 

When c = 0, both foci merge together with the centre of the ellipse and `a^2 = b^2`, i.e., a = b, and so the ellipse becomes circle in the above Fig.
Case (ii):

When c = a, then b = 0. The ellipse reduces to the line segment `F_1F_2` joining the two foci in above fig.

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