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AP EAMCET202318 May 2023Morning ShiftMathematicsCircleActual

The length of the chord of contact of the point (2,1) with respect to the circle x^2+y^2+4 x+2 y+1=0 is

Options

  1. A8 5
  2. B4 5
  3. C4 6 5
  4. D2 6 5

Correct answer

A. 8 5

Step-by-step solution

The given equation of circle is: aligned & x^2+y^2+4 x+2 y+1=0 & C (-2,-1), r= 4+1-1 =2 aligned The equation of chord of contact of point (2,1) is: aligned & 2 x+1 y+ 4(x+2) 2 + 2(y+1) 2 +1=0 & 2 x+y+2(x+2)+(y+1)+1=0 & 2 x+y+3=0 aligned aligned & CM = | -4-1+3 5 |= 2 5 & PM = CP ^2- CM ^2 & = 4- 4 5 aligned aligned & PM = 4 5 & PQ =2 PM =2 4 5 = 8 5 aligned

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