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AP EAMCET201920 Apr 2019Evening 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 at two distinct points, then

Options

  1. A2 < r < 8
  2. B1 < r < 9
  3. Cr = 2
  4. Dr = 8

Correct answer

A. 2 < r < 8

Step-by-step solution

Equation of given circles aligned S₁:(x-1)^2+(y-3)^2 & =r^2 and & S₂:(x-4)^2+(y+1)^2=3^2 aligned If circles S₁ and S₂ intersect at two distinct points, then |r₁-r₂ | 5 and |r-3| 2 and r-3 (-5,5) & r (-2,8) & 2 < r < 8 aligned Hence, option (a) is correct.

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