Find the area of the triangle formed by the lines joining the vertex of the parabola `x^(2) = -8y` to the ends of its latus rectum.

Explanation

To find the area of the triangle formed by the lines joining the vertex of the parabola \( x^2 = -8y \) to the ends of its latus rectum, follow these steps:

### Step 1: Identify the vertex and focus of the parabola
The given parabola is in the form \( x^2 = -4ay \). Here, we can see that \( 4a = 8 \), which gives us \( a = 2 \).

The vertex of the parabola is at the origin \( (0, 0) \). The focus, which is located at \( (0, -a) \), is at \( (0, -2) \).

### Step 2: Determine the endpoints of the latus rectum
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