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AP EAMCET201822 Apr 2018Morning ShiftMathematicsCircleActual

The pole of the straight line 9 x+y-28=0 with respect to the circle 2 x^2+2 y^2-3 x+5 y-7=0 is

Options

  1. A(3,1)
  2. B(3,-1)
  3. C(-3,1)
  4. D(4,-8)

Correct answer

B. (3,-1)

Step-by-step solution

Let (h, k) be the pole of the line 9 x+y-28= with respect to the circle x^2+y^2- 3 2 x+ 5 2 y- 7 2 =0 . Then, the equation of polar is aligned & polar is & h x+k y- 3 4 (x+h)+ 5 4 (y+k)- 7 2 =0 & x (h- 3 4 )+y (k+ 5 4 )- 3 4 h+ 5 4 k- 7 2 =0 & x(4 h-3)+y(4 k+5)-3 h+5 k-14=0 aligned This equation and 9 x+y-28=0 represent the same line. array lrr & 4 h-3 9 = 4 k+5 1 = -3 h+5 k-14 -28 = (say) h= & 3+9 4 , k= -5 4 ,-3 h+5 k-14=-28 & -3 ( 3+9 4 )+5 ( -5 4 )-14=-28 & -9-27 +5 -25-56=-112 & -22 -90=-112 & & 90 =90 =1 arra

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