(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 a, then where m1 and m2 are the slopes of L1 and L2, 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 (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