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AP EAMCET2014MathematicsCircle

The point at which the circles x^2+y^2-4 x-4 y+7=0 and x^2+y^2-12 x-10 y+45=0 touch each other, is

Options

  1. A( 13 5 , 14 5 )
  2. B( 2 5 , 5 6 )
  3. C( 14 5 , 13 5 )
  4. D( 12 5 , 2+ 21 5 )

Correct answer

C. ( 14 5 , 13 5 )

Step-by-step solution

Centres and radii of given circles are C₁(2,2), r₁= 2^2+2^2 -7=1 and C₂(6,5) , aligned r₂ & = 5^2+5^2-45 & = 36+25-45 =4 aligned Let P be the point at which the circle touch. Using internal ratio formula, P(x, y)= ( 1 6+4 2 1+4 , 1 5+4 2 1+4 ) = ( 6+8 5 , 5+8 5 )= ( 14 5 , 13 5 )

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