Find the length of the line segment joining the vertex of the parabola `y^2=4a x` and a point on the parabola where the line segment make and angle `theta` to the `x-a xi sdot`

Explanation

To find the length of the line segment joining the vertex of the parabola \( y^2 = 4ax \) and a point on the parabola where the line segment makes an angle \( \theta \) with the x-axis, we can follow these steps:

### Step 1: Identify the vertex and a point on the parabola
The vertex of the parabola \( y^2 = 4ax \) is at the origin, which is the point \( O(0, 0) \). Let the point on the parabola be \( P(x_1, y_1) \).

### Step 2: Relate the coordinates of point P to the angle \( \theta \)
Since the line segment \( OP \) makes an angle \( \theta \) with the x-axis, we can express the slope of the line segment as:
\[
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