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AP EAMCET2006MathematicsCircle

The number of common tangents to the two circles x^2+y^2-8 x+2 y=0 and x^2+y^2-2 x-16 y+25=0 is :

Options

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

Correct answer

B. 2

Step-by-step solution

The equations of circles are x^2+y^2-8 x+2 y=0 and x^2+y^2-2 x-16 y+25=0 The centre and radius of first circle are C₁(4,-1) and 17 respectively. Also the centre and radius of second circle are C₂(1,8) and 40 respectively. C₁ C₂= (1-4)^2+(8+1)^2 = 9+81 = 90 and r₁+r₂= 17 + 40 C₁ C₂ < r₁+r₂ These two circles internally Thus the number of common tangents is 2 .

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