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AP EAMCET2010MathematicsCircle

The equation of the circle concentric with the circle x^2+y^2-6 x+12 y+15=0 and of double its area is

Options

  1. Ax^2+y^2-6 x+12 y-15=0
  2. Bx^2+y^2-6 x+12 y-30=0
  3. Cx^2+y^2-6 x+12 y-25=0
  4. Dx^2+y^2-6 x+12 y-20=0

Correct answer

A. x^2+y^2-6 x+12 y-15=0

Step-by-step solution

The equation of the circle is S x^2+y^2-6 x+12 y+15=0 Let the equation of concentric circle of given circles, is S₂=x^2+y^2-6 x+12 y+15=0 On comparing the circle S₁ with, x^2+y^2+2 g x+2 f y+c=0 g=-3, f=6, c=15 Then, radius of circle is = g^2+f^2-c = 9+36-15 = 45-15 = 30 units and centre is (-g,-f)=(3,-6) Now, the area of the circle S is = (radius) ^2= ( 30 )^2=30 Let the radius of the concentric circle is r₂ . r₂= g^2+f^2-c = 9+36-c = 45-c Then, according to question, the area of concentric circle =2 area of S=2 3

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