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AP EAMCET202319 May 2023Morning ShiftMathematicsCircleActual

Let M ( -7 2 , -5 2 ) be the midpoint of the chord A B of the circle x^2+y^2+10 x+8 y-23=0 . If a x+ by 1=0 is the equation of A B then 3 a+3 b=

Options

  1. A6
  2. B1
  3. C36
  4. D-1

Correct answer

B. 1

Step-by-step solution

Let m₁ and m₂ be the slopes of line O M and line M B . Hence m₁= 4- 5 2 5- 7 2 =1 Since O M M B Hence m₁ m₂=-1 m₂=-1 Hence equation of line A B can be written as, aligned & (y+ 5 2 )=(-1) (x+ 7 2 ) & x+y+ 5 2 + 7 2 =0 & x+y+6=0 aligned 1 6 x+ 1 6 y+1=0 ...(i) But a x+b y+1=0 (given) is also the equation of chord A B Hence a= 1 6 , b= 1 6 3 a+3 b=3 ( 1 6 )+3 ( 1 6 )=1

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