If |z−2−3i|2+|z−4−3i|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 : |z−2−3i|2+|z−4−3i|2=λ Let z=x+iy, then (x−2)2+(y−3)2+(x−4)2+(y−3)2=λ⇒2x2+2y2−12x−12y=λ−38⇒x2+y2−6x−6y−λ−382=0 The minimum possible radius of the circle is 0, so √9+9+λ−382=0∴λ=2