Equations of locus

The circle x^2 +y^2 = 4 cuts the x-axis at the points A and B.
M(a,b) where b no equal to 0, is a variable point on the circle.
N is a point on the tangent to the circle at M such that AN _1_ NM.
AN and BM are then produced to meet at the point P.
Find,
a. the equations of the lines BM and AN in terms of a and b.
b. the coordinates of P in terms of a and b.
c. the equation of the locus of P when M moves