The centre of a circle which touches the line 2x - y = 1 at (1, 1) and also touches the line 2x + y = 4 is

JEE Advanced Mathematics question

The centre of a circle which touches the line at and also touches the line is

Answer: (A),(D)

The centre lies on the normal to at : . Since the circle touches both lines, the centre also lies on a bisector of the angles between them:

= ± \ ⇒\ 2y = 3 \ or \ 4x = 5.

- with : centre $(0,

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Question ID VK-110361