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AP EAMCET202421 May 2024Evening ShiftMathematicsCircleActual

The radical axis of the circles x^2+y^2+2 g x+2 f y+c=0 and 2 x^2+2 y^2+3 x+8 y+2 c=0 touches the circle x^2+y^2+2 x+2 y+1=0 . Then

Options

  1. Ag= 3 8 or f=1
  2. Bg= 2 3 or f=3
  3. Cg= 1 2 or f=1
  4. Dg= 3 4 or f=2

Correct answer

D. g= 3 4 or f=2

Step-by-step solution

Equation of radical axis is (2 g- 3 2 ) x+(2 f-4) y=0 Since x and y axis touch the circle x^2+y^2+2 x+2 y+1=0y= ( 2 g- 3 2 2 f-4 ) x touches the circle and passing through the origin. aligned & m=0 or m= & 2 g- 3 2 =0 g= 3 4 or 2 f-4=0 f=2 . aligned

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