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AP EAMCET2012MathematicsCircle

The equation to the line joining the centres of the circles belonging to the coaxial system of circles 4 x^2+4 y^2-12 x+6 y-3+ (x+2 y-6)=0 is

Options

  1. A8 x-4 y-15=0
  2. B8 x-4 y+15=0
  3. C3 x-4 y-5=0
  4. D3 x-4 y+5=0

Correct answer

A. 8 x-4 y-15=0

Step-by-step solution

Given coaxial system of circle is aligned & 4 x^2+4 y^2-12 x+6 y-3+ (x+2 y-6)=0 & or x^2+y^2-3 x+ 3 y 2 - 3 4 + 4 (x+2 y-6)=0 aligned Here, radical axis is x+2 y-6=0 . i.e., line of centre is 2 x-y+k=0 Here, centre of circle is ( 3 2 ,- 3 4 ) which lies on Eq. (i). array rlrl & & 2 ( 3 2 )+ 3 4 +k & =0 & 12+3 4 +k & =0 & k & =- 15 4 array Required equation is aligned 2 x-y- 15 4 & =0 8 x-4 y-15 & =0 aligned

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