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MHT CET202415 May 2024Morning ShiftMathematicsCircleActual

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

Options

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

Correct answer

C. 3

Step-by-step solution

aligned & x^2+y^2-x=0 & C ₁= ( 1 2 , 0 ), r ₁= (- 1 2 )^2+0^2-0 = 1 2 & x^2+y^2+x=0 & C ₂= (- 1 2 , 0 ), r ₂= ( 1 2 )^2+0^2-0 = 1 2 & C ₁ C ₂= ( 1 2 + 1 2 )^2+0^2 =1 & r ₁+ r ₂= 1 2 + 1 2 =1 & C ₁ C ₂= r ₁ r ₂ & The given circles touch each other externally. & Number of common tangents =3 aligned

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