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AP EAMCET202423 May 2024Morning ShiftMathematicsCircleActual

If the line through the point P(5,3) meets the circle x^2+y^2-2 x-4 y+ =0 at A (4,2) and B (x₁, y₁ ) , then P A P B is equal to

Options

  1. A6
  2. B12
  3. C9
  4. D8

Correct answer

D. 8

Step-by-step solution

Line through P(5,3) meets the circle x^2+y^2-2 x-4 y+ =0 at A(4,2) and B (x₁, y₁ ) A(4,2) lies on the circle 16+4-8-8+ =0 =-4 Eq. of circle becomes x^2+y^2-2 x-4 y-4=0 Also, equation of line passing P(5,3) and A(4,2) is (y-3)= 2-3 4-5 (x-5) x=2+y Put in equation of circle aligned & (2+y)^2+y^2-2(2+y)-4 y-4=0 & y^2-y-2=0 y=-1,2, So, x=1,4 & B (x₁, y₁ )=(1,-1) & P A P B= (5-4)^2+(3-2)^2 (5-1)^2+(3+1)^2 =8 aligned

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