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AP EAMCET202017 Sep 2020Evening ShiftMathematicsCircleActual

If the two circles ((x-1)^2+(y-3)^2=r^2 ) and (x^2+y^2-8 x+2 y+8=0 ) intersect in two different points, then what can we conclude about (r ) ?

Options

  1. A(r < 2 )
  2. B(r=2 )
  3. C(r>2 )
  4. D(2 < r < 8 )

Correct answer

D. (2 < r < 8 )

Step-by-step solution

As circles intersects in two distinct points So, ( |r₁-r₂ | < |C₁ C₂ | < r₁+r₂ ) ...(i) Here, ( C₁=(1,3), C₂=(4,-1) ) ( aligned C₁ C₂ & = (4-1)^2+(-1-3)^2 & = 9+16 =5 aligned ) ( Also, aligned r₂ & = g^2+f^2-C & = 42+1^2-8 & =3 aligned ) Hence, from Eq. (i), we have (2 < r < 8 ).

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