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KCET2011MathematicsCircle

The total number of common tangents of x²+y²-6 x-8 y+9=0 and x²+y²=1 is

Options

  1. A4
  2. B2
  3. C3
  4. D1

Correct answer

C. 3

Step-by-step solution

The given equation of circles and gathered x²+y²-6 x-8 y+9=0 x²+y²=1 gathered Radius and centre of both circles is C₁ (3,4), R₁= 9+16-9 =4C₂ (0,0), R₂=1C₁ C₂= (3-0)²+(4-0)² = 9+16 =5 R₁+R₂=4+1=5 C₁ C₂=R₁+R₂ distinct while the transverse tangents are coincident. So, number of comman tangents =3

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