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NTA Abhyas JEE Main2020MathematicsCirclePractice

The line 2 x - y + 1 = 0 touches a circle at the point 2 , 5 and the centre of the circle lies on x - 2 y = 4 . The diameter (in units) of the circle is

Options

  1. A6 5
  2. B10 3
  3. C4 5
  4. D10 2

Correct answer

A. 6 5

Step-by-step solution

tan ⁡ θ = 2 - 1 2 1 + 2 1 2 = 3 4 r 8 2 + 4 2 = tan ⁡ θ = 3 4 = r 4 5 ⇒ r = 3 5 ⇒ diameter = 6 5 units

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