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AP EAMCET2004MathematicsCircle

If P₁, P₂, P₃ are the perimeters of the three circles x^2+y^2+8 x-6 y=0 , 4 x^2+4 y^2-4 x-12 y-186=0 and x^2+y^2-6 x+6 y-9=0 respectively, then

Options

  1. AP₁ < P₂ < P₃
  2. BP₁ < P₃ < P₂
  3. CP₃ < P₂ < P₁
  4. DP₂ < P₃ < P₁

Correct answer

B. P₁ < P₃ < P₂

Step-by-step solution

Given circle are x^2+y^2+8 x-6 y=0 gathered 4 x^2+4 y^2-4 x-12 y-186=0 and x^2+y^2-6 x+6 y-9=0 . gathered Let r₁, r₂ and r₃ be the radius of the respective circle, then aligned & r₁= (-4)^2+(-3)^2+0 = 25 =5 & r₂= ( 1 2 )^2+ ( 3 2 )^2+ ( 186 4 ) = 49 =7 & r₃= (3)^2+(3)^2+9 = 27 =3 3 & P₁=2 r₁=10 & P₂=2 r₂=14 & P₃=2 r₃=6 3 & P₁ < P₃ < P₂ aligned

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