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AP EAMCET202418 May 2024Morning ShiftMathematicsCircleActual

If 2 x-3 y+3=0 and x+2 y+k=0 are conjugate lines with respect to the circle S x^2+y^2+8 x-6 y-24=0 , then the length of the tangent drawn from the point ( k 4 , k 3 ) to the circle S =0 is

Options

  1. A7
  2. B1
  3. C12
  4. D24

Correct answer

B. 1

Step-by-step solution

aligned & Given equation of circle x^2+y^2+8 x-6 y-24=0 & (x+4)^2+(y-3)^2=24+25=49 aligned So, centre =(-4,3) , radius =7 Since, 2 x-3 y+3=0 and x+2 y+k=0 are conjugate lines with respect to the given circle. So, 7^2(1 2+2 (-3))=(2 (+4)+(-3) (-3)-3)(1 (+4)+2 (-3)-k) k=12 Now, ( k 4 , k 3 )=(3,4) AO = (3+4)^2+(4-3)^2 = 50 Since, In APO ; AP = 50-49 =1

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