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Question

If |z23i|2+|z43i|2=λ represents a equation of circle, then the value of λ when the radius of circle is minimum, is

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Solution

Given : |z23i|2+|z43i|2=λ
Let z=x+iy, then
(x2)2+(y3)2+(x4)2+(y3)2=λ2x2+2y212x12y=λ38x2+y26x6yλ382=0
The minimum possible radius of the circle is 0, so
9+9+λ382=0λ=2

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