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If |z-2-3i|^(2) + |z- 5 - 7i|^(2)= lamb...

If `|z-2-3i|^(2) + |z- 5 - 7i|^(2)= lambda` respresents the equation of circle with least radius, then find the value of `lambda`.

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We have
`|z-(2+3i)|^(2)+|z-(5+7i)|^(2)=lambda`

Clearly, this represents the equation of circle with lest radius if `(2+3i)` and `(5+7i)` are end points of diameter of the circle.
`:." "lambda=|(2+3i)-(5+7i)|^(2)=|-3-4i|^(2)=5^(2)=25`
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