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AP EAMCET201922 Apr 2019Morning ShiftMathematicsCircleActual

The equation of the circle which cuts the circles ( aligned & S₁ x^2+y^2-4=0 & S₂ x^2+y^2-6 x-8 y+10=0 & S₃ x^2+y^2+2 x-4 y-2=0 aligned ) at the extremities of diameters of these circles is

Options

  1. A(x^2+y^2-4 x-6 y-4=0 )
  2. B(x^2+y^2+4 x-4=0 )
  3. C(x^2+y^2=25 )
  4. D(x^2+y^2+x+y+1=0 )

Correct answer

A. (x^2+y^2-4 x-6 y-4=0 )

Step-by-step solution

Let the equation of required circle is (S x^2+y^2+2 g x+2 f y+c=0 ) and equation of given circles ( aligned & S₁ x^2+y^2-4=0 & S₂ x^2+y^2-6 x-8 y+10=0 & S₃=x^2+y^2+2 x-4 y-2=0 aligned ) ( ) Circle (S=0 ) cuts the circles (S₁=0, S₂=0 ) and (S₃=0 ) at the extermities of the diameters, so common chord of (S=0 ) and (S₁=0 ) passes through the centre of the circle (S₁=0 ), so (c=-4 ) Similarly ((2 g+6) x+(2 f+8) y-14=0 ) passes through ((3,4) ), so (6 g+8 f+36=0 ) ( 3 g+4 f+18=0 )...(i) and ((2 g-2) x+(2 f+4) y-2=0 ), p

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