Question 1190881
Here's how to find the equation of the ellipse:

1. **Find the Center:** The center of the ellipse is the midpoint of the line segment connecting the vertices.  The midpoint formula is ((x₁ + x₂)/2, (y₁ + y₂)/2).

   Center = ((-1 + 5)/2, (3 + 3)/2) = (2, 3)

2. **Determine the Orientation:** Since the vertices have the same y-coordinate, the major axis is horizontal.

3. **Find 'a' (Semi-major Axis):** The semi-major axis is the distance from the center to a vertex.

   a = distance from (2, 3) to (5, 3) = |5 - 2| = 3

4. **Find 'b' (Semi-minor Axis):** The length of the minor axis is given as 4. The semi-minor axis is half of this length.

   b = 4 / 2 = 2

5. **Write the Equation:** The general equation of an ellipse centered at (h, k) with a horizontal major axis is:

   (x - h)² / a² + (y - k)² / b² = 1

   Substitute the values we found (h = 2, k = 3, a = 3, b = 2):

   (x - 2)² / 3² + (y - 3)² / 2² = 1

   Simplify:

   (x - 2)² / 9 + (y - 3)² / 4 = 1

Therefore, the equation of the ellipse is (x - 2)²/9 + (y - 3)²/4 = 1.