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AP EAMCET201824 Apr 2018Morning ShiftMathematicsCircleActual

The number of common tangents to the circles x^2+y^2-4 x-2 y+k=0 and x^2+y^2-6 x-4 y+l=0 , having radii 2 and 3 respectively, is

Options

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

Correct answer

B. 2

Step-by-step solution

Given circle are, gathered x^2+y^2-4 x-2 y+k=0 Centre c₁(2,1) and r₁=2 x^2+y^2-6 x-4 y+l=0 gathered Centre c₂(3,2) and r₂=3 aligned c₁ c₂ & = (2-3)^2+(1-2)^2 & = 1+1 = 2 c₁ c₂ & < r₁+r₂ aligned So, circles have two common tangents.

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