Let the two sources S, and Sz shown in Fig. 35.3 be located at y = d and y = -d, respectively. 

(a) Rewrite Eq. (35.1) in terms of the x- and y-coordinates of a point P in Fig. 35.3 at which constructive interference occurs. 

(b) Your expression in part (a) is the equation for the antinodal curves shown in Fig. 353. Show that these curves are hyperbolas. (Hint: You may want to review the definition of a hyperbola in analytic geometry.) 

(c) Repeat part (a) for Eq. (35.2), which describes points at which destructive interference occurs, and show that the nodal curves (not shown in Fig. 353) are also hyperbolas.