Find the equation of the ellipse whose centre is (-2,3) and whose semi axes are 3 and 2 when major axis is (i.) parallel to x-axis (ii.) parallel to y-axis.

Explanation

To find the equation of the ellipse with center (-2, 3) and semi-axes 3 and 2, we will consider two cases: (i) when the major axis is parallel to the x-axis, and (ii) when the major axis is parallel to the y-axis.

### Case (i): Major Axis Parallel to the x-axis

1. **Identify the center and semi-axes**:
- Center: (-2, 3)
- Semi-major axis (a): 3 (since it is greater than the semi-minor axis)
- Semi-minor axis (b): 2
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