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AP EAMCET202421 May 2024Morning ShiftMathematicsStraight LinesActual

P is a variable point such that the distance of P from A(4,0) is twice the distance of P from B(-4,0) . If the line 3 y-3 x-20=0 intersects the locus of P at the points C and D , then the distance between C and D is

Options

  1. A8
  2. B8 2 3
  3. C32 3
  4. D8 3

Correct answer

C. 32 3

Step-by-step solution

aligned & (x-4)^2+y^2 =2 (x+4)^2+y^2 & 3 x^2+3 y^2+40 x+48=0 & Centre ( -20 3 , 0 ) ; Radius = ( 20 3 )^2-16 = 16 3 aligned Given line is 3 y-3 x-20=0 It passes through ( -20 3 , 0 ) i.e. the centre. Distance between C & D = Diameter = 32 3

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