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AP EAMCET202316 May 2023Morning ShiftMathematicsCircleActual

If the length of the chord 2 x+3 y+k=0 of the circle x^2+y^2-6 x-8 y+9=0 is 2 3 , then one of the values of k is

Options

  1. A31
  2. B5
  3. C-5
  4. D-13

Correct answer

C. -5

Step-by-step solution

The given equation of circle is x^2+y^2-6 x-8 y+9=0 Its centre is C=(3,4) and Radius R= 9+16-9 R= 16 =4 A B=2 3 A M= A B 2 = 2 3 2 = 3 And C M= 2 3+4 3+k 4+9 = 18+k 13 In A C M, A C^2=C M^2+A M^2 aligned & 4^2= ( 18+k 13 )^2+( 3 )^2 & 16-3= ( 18+k 13 )^2 & 18+k 13 = 13 18+k=13 k=-5 aligned

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