Q: If the equation |z-z_{1}|^{2} +|z-z_{2}|^{2} = k , represents the equation of a circle, where z_{1} = 2 + 3i, z_{2} = 4 + 3i are the extremities of a diameter, then the value of k is

(A) 1/ 4

(B) 4

(C) 2

(D) None of these

Sol. As z_{1} and z_{2} are the extremities of the diameter,

⇒ |z – z_{1}|^{2} +|z – z_{2}|^{2} = |z_{1} – z_{2}|^{2}

⇒ k = |z_{1} – z_{2}|^{2} = | 2 + 3i – 4 – 3i|^{2} = |-2|^{2} = 4

Hence (B) is the correct answer.