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The number of solutions of the simultaneous complex equations |z-3-i|=2 and |z-2+i|+|z-4-3 i|=6 is

Correct answer

2

Step-by-step solution

|z-3-i|=2 represents a circle with centre 3+i and radius 2 |z-2+i|+|z-4-3 i|=6 represents an ellipse with centre ( 2-i+4+3 i 2 )=3+i and major axis =6 Also, the distance between foci =2 5 aligned & eccentricity = 2 5 6 = 5 3 1 & Minor axis =2 3 1- 5 a =4 aligned diameter of circle = minor axis So, the circle touches the ellipse internally

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