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.
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.
When c = a, then b = 0. The ellipse reduces to the line segment `F_1F_2` joining the two foci in above fig.
Find the equation of the ellipse whose centre is (−2, 3) and whose semi-axis are 3 and 2 when major axis is (i) parallel to x-axis (ii) parallel to y-axis.