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KCET2010MathematicsCircle

Two circles centred at (2,3) and (5,6) intersect each other. If the radii are equal, the equation of the common chord is

Options

  1. Ax + y +1=0
  2. Bx-y+1=0
  3. Cx+y-8=0
  4. Dx-y-8=0

Correct answer

C. x+y-8=0

Step-by-step solution

Let the radius of both circles are ' r '. Now, equation of circle with centre at (2,3) is S₁ (x-2)²+(y-3)²=r² ...(i) and equation of circle with centre at (5,6) is S₂ (x-5)²+(y-6)²=r² ...(ii) Now, the equation common chord gathered Radical axis of S ₁ and S ₂=0 ( S ₁- S ₂ )=0 [( x -2)² ]+ [( y -3)² ] -[( x -5)]²-[( y -6)]²=0 x ²+ y ²+4-4 x +9-6 x - x ²- y ²-25-36+10 x +12 y =0 6 x +6 y -48=0 Common chord x + y -8=0 gathered

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