Find the area of the parabola `y^2=4a x`bounded by its latus rectum.

Explanation

To find the area of the parabola \( y^2 = 4ax \) bounded by its latus rectum, we can follow these steps:

### Step 1: Understand the Parabola and Latus Rectum
The given parabola is \( y^2 = 4ax \). The latus rectum of this parabola is a vertical line that passes through the focus of the parabola. The focus of the parabola \( y^2 = 4ax \) is at the point \( (a, 0) \). The equation of the latus rectum is given by \( x = a \).

### Step 2: Find the Points of Intersection
To find the area bounded by the parabola and the latus rectum, we need to determine the points where the parabola intersects the line \( x = a \):
- Substitute \( x = a \) into the parabola's equation:
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