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JEE Main202227 Jul 2022Morning ShiftMathematicsCircleActual

If the circle x 2 + y 2 - 2 g x + 6 y - 19 c = 0 , g , c ∈ ℝ passes through the point 6 , 1 and its centre lies on the line x - 2 c y = 8 , then the length of intercept made by the circle on x -axis is

Options

  1. A11
  2. B4
  3. C3
  4. D2 23

Correct answer

D. 2 23

Step-by-step solution

Given circle x 2 + y 2 - 2 g x + 6 y - 19 c = 0 Also given circle passes through 6 , 1 So, 12 g + 19 c = 43           ⋯ 1 And centre g , - 3 lies on x - 2 c y = 8 , So, g + 6 c = 8             … 2 On solving equation 1 and 2 we get, c = 1 and g = 2 Now equation of circle will be, x 2 + y 2 - 4 x + 6 y - 19 = 0 Now length of intercept on x -axis is given by = 2 g 2 - C = 2 2 2 + 19 = 2 23

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