Question

${|z-2-3i|}^2+{|z-4-3i|}^2=\lambda$ represents the equation of a circle with least radius. Find the value of $\lambda$.

Answer 1

If $P\left(z\right)$ lies on a circle and $P{B}^2+P{A}^2=\lambda$ (constant),
then $\lambda =A{B}^2⟹\lambda =4$.
Ans: 4