If the angle between the normal to the parabola `y^(2)=4ax` at point P and the focal chord passing through P is `60^(@)`, then find the slope of the tangent at point P.

Explanation

To solve the problem, we need to find the slope of the tangent to the parabola \( y^2 = 4ax \) at point \( P \) given that the angle between the normal at \( P \) and the focal chord through \( P \) is \( 60^\circ \).

### Step-by-Step Solution:

1. **Identify the Parabola and Given Information**:
The equation of the parabola is given as \( y^2 = 4ax \). We know that the focus of this parabola is at the point \( (a, 0) \).

2. **Understanding the Geometry**:
...