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AP EAMCET201920 Apr 2019Morning ShiftMathematicsCircleActual

Suppose that the circle (x^2+y^2+2 g x+2 f y+c=0 ) has its centre on (2 x+3 y-7=0 ) and cuts the circles (x^2+y^2-4 x-6 y+11=0 ) and (x^2+y^2-10 x-4 y+21=0 ) orthogonally. Then (5 g-10 f+3 c= )

Options

  1. A0
  2. B1
  3. C3
  4. D9

Correct answer

D. 9

Step-by-step solution

The equation of given circle (x^2+y^2+2 g x+2 f y+c=0 ) ...(i) having centre ((-g,-f) ) lying on the line ( aligned & 2 x+3 y-7=0 & so 2 g+3 f+7=0 (ii) aligned ) Since circle (i) cuts the given circles ( aligned x^2+y^2-4 x-6 y+11 & =0 and x^2+y^2-10 x-4 y+21 & =0 aligned ) orthogonally ( array lc so, & 2 g(-2)+2 f(-3)=c+11 & 4 g+6 f+c+11=0 (iii) and & 2 g(-5)+2 f(-4=c+21 & 10 g+4 f+c+21=0 (iv) array ) From Eqs. (iii) and (iv), we get (6 g-2 f+10=0 (v) ) From Eq. (ii) and (v), we get ( gathered 11 f+11=0 f=-1 So, g

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