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AP EAMCET201920 Apr 2019Evening ShiftMathematicsCircleActual

The number of common tangents to the circles x^2+y^2+4 x-6 y-12=0 and x^2+y^2-8 x+10 y+5=0 is

Options

  1. A4
  2. B3
  3. C2
  4. D1

Correct answer

C. 2

Step-by-step solution

Equation of given circles array r S₁: x^2+y^2+4 x-6 y-12=0 and S₂: x^2+y^2-8 x+10 y+5=0 array Centre of S₁ is C₁(-2,3) and radius of S₁ is r₁=5 and centre of S₂ is C₂(4,-5) and radius of S₂ is r₂=6 . aligned & C₁ C₂= (4+2)^2+(-5-3)^2 = 36+64 =10 & and r₁+r₂=5+6=11 & r₁+r₂>c₁ c₂ aligned There are only two common tangent to circle S₁ and S₂ . Hence, option (c) is correct.

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