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AP EAMCET202124 Aug 2021Evening ShiftMathematicsCircleActual

If S=x^2+y^2+2 x+17 y+4=0S^ =x^2+y^2+7 x+6 y+11=0 and S^ =x^2+y^2-x+22 y+3=0 are three circles, then the length of tangent from their radical center to S=0 is ......... units.

Options

  1. A53
  2. B57
  3. C15
  4. D17

Correct answer

B. 57

Step-by-step solution

Given, S=x^2+y^2+2 x+17 y+4=0S^ =x^2+y^2+7 x+6 y+11=0S=x^2+y^2-x+22 y+3=0S-S^ =5 x-11 y+7=0 ...(i) S^ -S^ =8 x-16 y+8=0x-2 y+1=0 ...(ii) Solving Eqs. (i) and (ii), we get (3,2) Radical centre of circle is (3,2) . Length of tanget from (3,2) to S is S₁ = (3)^2+(2)^2+2(3)+17(2)+4 = 57

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