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AP EAMCET201922 Apr 2019Morning ShiftMathematicsCircleActual

The circle (S=0 ) cuts the circle (x^2+y^2-4 x+2 y-7=0 ) orthogonally. If ((2,3) ) is the centre of the circle (S=0 ), then its radius is

Options

  1. A2
  2. B1
  3. C3
  4. D4

Correct answer

A. 2

Step-by-step solution

Given that, (S=0 ) circle cuts the circle (x^2+y^2-4 x+2 y-7=0 ) orthogonally and centre of circle (S=0 ) is ((2,3) ). As we know that, if two circles intersect orthogonally, Then, (2 g g^ +2 f f^ =c+c^ ) Here, ((g, f)=(2,3) ) and ( (g^ , f^ )=(2,-1) ) ( array rlrl & c^ =-7 & 2(-2)(2)+2(3)(-1)=c-7 & 8-6 =c-7 & 2 =c-7 & c =9 & Now, required radius = (2)^2+(3)^2-9 & = 4+9-9 = 4 =2 array )

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