(a) State the formula for determining the angle between the intersection of two lines.
(b) Show that the angle bisector line: y = Mx between the lines y = m1*x and y = m2*x is given by (M - m1)(1 + M*m2) = (m2 - M)(1 + M*m1).
(c) Hence show that the gradients of the two angle bisector lines is given by the quadratic in M:
(m1 + m2)M^2 + 2(1-m1*m2)M - (m1 + m2) = 0.
(d) State the product of the roots of this equation. Hence deduce the relationship between these two angle bisectors.
N.B. the 1 and 2 in m1 and m2 are the bases of m (like in logs).
Could someone please please show me how to do this question?