AB is a chord of the parabola `y^2 = 4ax` with its vertex at A. BC is drawn perpendicular to AB meeting the axis at C.The projecton of BC on the axis of the parabola is

Options

A. a
B. 2a
C. 4a
D. 8a

Explanation

To solve the problem, we need to find the projection of the line segment BC on the axis of the parabola given that AB is a chord of the parabola \(y^2 = 4ax\) with its vertex at point A, and BC is drawn perpendicular to AB meeting the axis at point C.

### Step-by-Step Solution:

1. **Identify the Coordinates of Point B**:
Let the coordinates of point B on the parabola be \(B(at^2, 2at)\), where \(t\) is a parameter.

2. **Find the Slope of Chord AB**:
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