The centres of a set of circles, each of radius 3 , lie on the circle x^2 + y^2 = 25. The locus of any point in the set is

JEE Main 2002 Mathematics question

The centres of a set of circles, each of radius 3 , lie on the circle . The locus of any point in the set is

(1)Correct
(2)
(3)
(4)

Answer: (1)

Solution

Each centre is at distance 5 from the origin, and a point of a circle of radius 3 is at distance 3 from its centre. By the triangle inequality, the distance of any point of these circles from the origin

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Question ID VK-038018