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MHT CET202620 April 2026Evening ShiftMathematicsCircleActual

The equation of a circle whose center lies on x + 2y = 0 and touching the lines 3x - 4y + 8 = 0 and 3x - 4y - 28 = 0 is

Options

  1. A(x - 2)^2 + (y + 1)^2 = 324
  2. B(x - 2)^2 + (y - 1)^2 = 324
  3. C5(x - 2)^2 + 5(y + 1)^2 = 324
  4. D25(x - 2)^2 + 25(y + 1)^2 = 324

Correct answer

D. 25(x - 2)^2 + 25(y + 1)^2 = 324

Step-by-step solution

The given lines 3x - 4y + 8 = 0 and 3x - 4y - 28 = 0 are parallel. The distance between them is the diameter of the circle. Diameter = |8 - (-28)| 3^2 + (-4)^2 = 36 5 Radius r = 18 5 The center of the circle lies on the line parallel to and midway between the two given lines. The equation of this midway line is: 3x - 4y + 8 + (-28) 2 = 0 3x - 4y - 10 = 0 The center also lies on the given line x + 2y = 0 . Solving 3x - 4y - 10 = 0 and x + 2y = 0 , we substitute x = -2y : 3(-2y) - 4y - 10 = 0 -10y = 10 y = -1 Substit

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