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COMEDK2012MathematicsCircle

The number of common tangents to the circles x²+y²-2 x-4 y+1=0 and x²+y²-12 x-16 y+91=0 is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

D. 4

Step-by-step solution

We have, x²+y²-2 x-4 y+1=0 and x²+y²-12 x-16 y+91=0 Here, C₁ (1,2) and r₁= 1+4-1 =2 and C₂ (6,8) and r₂= 36+64-91 =3 Now, C₁ C₂= 25+36 = 61 Here, r₁+r₂=5 < 61 So, circle are far apart. Hence, number of common tangents is 4 .

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