A circle touches each of the lines x-y=0 and x+y=0 at unit distance from the origin. The centre of the circle may be at

NDA 2026 Mathematics question

A circle touches each of the lines and at unit distance from the origin. The centre of the circle may be at

(A)Correct
(B)
(C)
(D)

Answer: (A)

Solution

The two lines are perpendicular and meet at the origin ; the centre lies on a bisector of the angle between them, i.e. on a coordinate axis. Take . The line makes with each tangent line,

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Question ID VK-030422