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KCET2009MathematicsCircle

The number of common tangents to the circles x ²+ y ²- y =0 and x ²+ y ²+ y =0 is

Options

  1. A2
  2. B3
  3. C0
  4. D1

Correct answer

B. 3

Step-by-step solution

Given circles are x ²+ y ²- y =0 and x ²+ y ²+ y =0 centres and radii of these circles are C₁ (0, 1 2 ), C₂ (0,- 1 2 ) and r₁= 1 2 , r₂= 1 2 Now, C₁ C₂= 0+ ( 1 2 + 1 2 )² =1 and C ₁ C ₂= r ₁+ r ₂ It means that two circles touch each other externally. Hence, number of common tangents are 3 .

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