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AP EAMCET202419 May 2024Evening ShiftMathematicsCircleActual

The circle S x^2+y^2-2 x-4 y+1=0 cuts the y -axis at A , B ( OA OB ) . If the radical axis of S O and S ^ x^2+y^2-4 x-2 y+4=0 cuts the y -axis at C then the ratio in which C divides AB is

Options

  1. A7+2 3 :-7+2 3
  2. B3 +2: 3 -2
  3. C6-2 3 : 2 3 -6
  4. D-3: 3

Correct answer

A. 7+2 3 :-7+2 3

Step-by-step solution

Given, S x^2+y^2-2 x-4 y+1=0 If x=0 y^2-4 y+1=0 y= 4 16-4 2 =2 3 So, A(0,2+ 3 ) and B(0,2- 3 ) Now, equation of radical axis is S-S^ =0 2 x-2 y-3=0 If x=0 -2 y=3 y= -3 2 So, C (0, -3 2 ) Let the required ratio be K: 1 aligned & So, -3 2 = K(2- 3 )+1(2+ 3 ) K+1 & -3 K-3=4 K-2 K 3 +4+2 3 & K(-7+2 3 )=7+2 3 & K: 1=(7+2 3 ):(-7+2 3 ) aligned

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