(a) Use the identity for tan(x - y) (see Equation 14b in Appendix D) to show that if two lines L1 and L2 intersect at an angle α, then
tan α = m2 - m1 / 1 + m1m2
where and are the slopes of and , respectively.
(b) The angle between the curves C1 and C2 at a point of intersection P is defined to be the angle between the tangent lines to C1 and C2 at P (if these tangent lines exist). Use part (a) to find, correct to the nearest degree, the angle between each pair of curves at each point of intersection.
(i) y = x2 and y = (x - 2)2
(ii) x2 - y2 = 3 and x2 - 4x + y2 + 3 = 0