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KVPY2013MathematicsCircle

Two line segments AB and CD are constrained to move along the x and y axes, respectively, in such a way that the points A, B, C, D are concyclic. If A B=a and C D=b , then the locus of the centre of the circle passing through A, B, C, D in polar coordinates is

Options

  1. Ar²= a²+b² 4
  2. Br² 2 = a²-b² 4
  3. Cr²=4 (a²+b² )
  4. Dr² 2 =4 (a²-b² )

Correct answer

B. r² 2 = a²-b² 4

Step-by-step solution

array l 2 g²-c =a 2 f²-c =b array Polar coordinates of centre of circle be ( , r ) array ll g=-r and g²-f²= a²-b² 4 f=-r r² 2 = a²-b² 4 array

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