Question 1190882
Here's how to determine the equation of the ellipse:

**1. Identify the Center:**

The center is given as (0, 0).

**2. Determine the Orientation:**

Since a vertex is at (0, -6), which lies directly below the center, the major axis is vertical.

**3. Find 'a' (Semi-major Axis):**

The distance from the center (0, 0) to the vertex (0, -6) is 6 units.  Therefore, a = 6.

**4. Find 'b' (Semi-minor Axis):**

The end of the minor axis is at (4, 0). The distance from the center (0, 0) to this point is 4 units. Therefore, b = 4.

**5. Write the Equation:**

The general equation of an ellipse centered at (h, k) with a vertical major axis is:

(x - h)² / b² + (y - k)² / a² = 1

Substitute the values we found (h = 0, k = 0, a = 6, b = 4):

(x - 0)² / 4² + (y - 0)² / 6² = 1

Simplify:

x² / 16 + y² / 36 = 1

Therefore, the equation of the ellipse is x²/16 + y²/36 = 1.