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AP EAMCET20225 Jul 2022Morning ShiftMathematicsCircleActual

The radius of the circle having 3 x-4 y+4=0 and 6 x-8 y-7=0 as its tangents is

Options

  1. A3 2
  2. B3
  3. C6
  4. D3 4

Correct answer

D. 3 4

Step-by-step solution

Equation of the given tangents are aligned & E₁=3 x-4 y+4=0 & E₂=6 x-8 y-7=0 aligned 3 x-4 y- 7 2 =0 Here, a=3, b=-4 c₁=4, c₂= -7 2 Since, slopes of the given tangents are equal, i.e. 3 4 . The given tangents are parallel, d= | c₂-c₁ a^2+b^2 |= | 4- ( -7 2 ) 3^2+(-4)^2 |d= 15 2 9+16 = 15 2 5 = 3 2 As we know that distance between two parallel tangents of a circle is equal to the diameter of that circle. Diameter of given circle = 3 2 Radius of the given circle = Diameter 2 = ( 3 / 2 2 )= 3 4

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