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AP EAMCET20225 Jul 2022Morning ShiftMathematicsCircleActual

The radical centre of the three circles x^2+y^2-1=0, x^2+y^2-8 x+15=0 and x^2+y^2+10 y+24=0 is

Options

  1. A(2, -5 2 )
  2. B(2, 5 2 )
  3. C(-2, 5 2 )
  4. D(-2, -5 2 )

Correct answer

A. (2, -5 2 )

Step-by-step solution

Let S₁: x^2+y^2-1=0 ...(i) S₂: x^2+y^2-8 x+15=0 ...(ii) and S₃: x^2+y^2+10 y+24=0 ...(iii) From Eqs. (i) and (ii), 8 x-15=1 x=2 Now, from Eqs. (i) and (iii), -10 y-24=1 -10 y=25 y= -5 2 Hence, the radical centre is (2, -5 2 ) .

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