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AP EAMCET201920 Apr 2019Evening ShiftMathematicsCircleActual

The equation of the circle which cuts the circles x^2+y^2+4 x-7=0 , 2 x^2+2 y^2+3 x+5 y-9=0, x^2+y^2+y=0 orthogonally is

Options

  1. Ax^2+y^2-4 x-2 y-1=0
  2. Bx^2+y^2-4 x-6 y-3=0
  3. Cx^2+y^2-4 x-2 y-3=0
  4. Dx^2+y^2-2 x-4 y-1=0

Correct answer

A. x^2+y^2-4 x-2 y-1=0

Step-by-step solution

The centre of the circle which cuts the given circles having equation aligned & S₁: x^2+y^2+4 y-7=0 & S₂: 2 x^2+2 y^2+3 x+5 y-9=0 aligned and S₃: x^2+y^2+y=0 is radical centre of circles S₁, S₂ and S₃ . Equation of radical axis of circles S₁ and S₂ is So, coordinate of radical centre is (2,1) and radius of required circle is equals to length of tangent drawn from radical centre (2,1) to any one of the circle = 4+1+8-7 = 6 So, equation of required circle is : aligned (x-2)^2+(y-1)^2 & =6 x^2+y^2-4 x-2 y-1 & =0 . ali

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