2. Calculate the coordinates of the points of intersection between all lines and the circle. If the line is a tangent then there exists only one point 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.