If the line `y=sqrt(3)x+k` touches the circle `x^2+y^2=16 ,` then find the value of `kdot`

Explanation

To solve the problem, we need to find the value of \( k \) such that the line \( y = \sqrt{3}x + k \) touches the circle defined by the equation \( x^2 + y^2 = 16 \).

### Step-by-step Solution:

1. **Identify the Circle's Properties**:
The equation of the circle is \( x^2 + y^2 = 16 \).
- The center of the circle is at \( (0, 0) \).
- The radius \( r \) of the circle is \( \sqrt{16} = 4 \).
...