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AP EAMCET20224 Jul 2022Morning ShiftMathematicsCircleActual

The Locus of centers of the circles, possessing the same area and having 3 x - 4 y + 4 = 0 and 6 x - 8 y - 7 = 0 as their common tangent, is

Options

  1. A12 x - 16 y - 15 = 0
  2. B3 x - 4 y + 11 2 = 0
  3. C12 x - 16 y + 15 = 0
  4. D3 x - 4 y - 11 2 = 0

Correct answer

C. 12 x - 16 y + 15 = 0

Step-by-step solution

Given, 3 x - 4 y + 4 = 0 and 6 x - 8 y - 7 = 0 are common tangent, Now the given lines are parallel tangents to a circle, So, the diameter of the circle is equal to the distance between these lines, So that the required radius is 1 2 × 4 + 7 2 9 + 16 = 1 2 × 15 2 × 1 5 = 3 4 The center of the circle lies on the line parallel to the given lines at a distance of 3 4 from each of them. So let the equation passing from center be 3 x - 4 y + k = 0             ⋯ 1 Then b

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