Let z1 and z2 be two distinct points in the complex plane, and let K be a positive real constant that is less than the distance between z1 and z2.
(a) Show that the set of points {z:∣z−z1∣−∣z−z2∣=K} is a hyperbola with foci z1 and z2.
(b) Find the equation of the hyperbola with foci ±2 that goes through the point 2+3i.
(c) Find the equation of the hyperbola with foci ±25 that goes through the point 7+24i.