1. All lines with the equation pass through the point P(4,0).

2. Calculate the coordinates of the points of intersection between all lines and the circle. If the line is a tangent then there exists onlyonepoint of intersection, that means the discriminante must be zero:

Plug in the linear term for y into the 1st equation:

Solve for x:

As stated before the discriminant must be zero:

3. Plug in this value into the equation of the line.

I've attached a sketch of the circle and the 2 tangents.