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AP EAMCET202419 May 2024Evening ShiftMathematicsCircleActual

If the circles S x^2+y^2-14 x+6 y+33=0 and S ^ x^2+y^2-a^2=0(a ~N ) have 4 common tangents then possible number of values of a is

Options

  1. A13
  2. B5
  3. C14
  4. D2

Correct answer

D. 2

Step-by-step solution

Given, S (x-7)^2+(y+3)^2=5^2 So C=(7,-3), r=5 and S^ x^2+y^2=a^2 C^ =(0,0), r^ =a Since, for 4 common tangent C C^ +r^ 58 5+a a 7.616-5 a 2.616 So, a=2 .

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