Find the equation of the ellipse, the co-ordinates of whose foci are `(0, pm4)` and eccentricity `(4)/(5)`

Explanation

To find the equation of the ellipse given the coordinates of its foci and its eccentricity, we can follow these steps:

### Step 1: Identify the coordinates of the foci
The coordinates of the foci are given as (0, ±4). This indicates that the foci are located on the y-axis. Therefore, we have:
- \( c = 4 \)

### Step 2: Determine the major axis
Since the foci are on the y-axis, the major axis of the ellipse is also along the y-axis. The standard form of the equation of an ellipse with a vertical major axis is:
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