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AP EAMCET202420 May 2024Morning ShiftMathematicsCircleActual

If power of a point (4,2) with respect to the circle x^2+y^2-2 x+6 y+ ^2-16=0 is 9 , then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is

Options

  1. A16+4 6
  2. B16+4 6 -6 2
  3. C16+4 6 +6 2
  4. D16+6 2

Correct answer

A. 16+4 6

Step-by-step solution

x^2+y^2-2 x+6 y+ ^2-16=0 Centre (C)=( ,-3) ;(x- )^2+(y+3)^2=25 Radius (R)=5d= distance between centre and (4,2) d^2=( -4)^2+25 Power =d^2-R^2 9=( -4)^2 ~m =1,7 When =1:(x-1)^2+(y+3)^2=25 Put x=0 (y+3)^2=24 y^2+6 y-15=0 y=-3 2 6 Put y=0 (x-1)^2=16 x=5,-3 When =7:(x-7)^2+(y+3)^2=25 put y=0 (x-7)^2=16 x=11,3 Sum of length of intercept =16+4 6

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