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AP EAMCET202317 May 2023Morning ShiftMathematicsCircleActual

The polar of a point with respect to the circle x^2+y^2-10 x+12 y-3=0 which is not a tangent and not a chord of contact is

Options

  1. A2 x+3 y+8=0
  2. B3 x+4 y+5=0
  3. C5 x-12 y+7=0
  4. D6 x-8 y+15=0

Correct answer

D. 6 x-8 y+15=0

Step-by-step solution

Given equation of circle is x^2+y^2-10 x+12 y-3=0 g=-5, f=6, c=-3 centre =(5,-6) and r=8 We know that that pole of polar A x+B y+C=0 w.r to circle x^2+y^2+2 g x+2 f y+c=0 can be find out by x₁+g A = y₁+f B = g x₁+t y₁+c c from option (d) A=6, B=-8, C=15 x₁-5 6 = y₁+6 -8 = -5 x₁+6 y₁-3 15 15 x₁-12 y₁=19... (i) and 40 x₁-63 y₁=66... (ii) From equations (i) and (ii), we get x₁= 135 155 , y₁= -46 93 Now, distance of pole from centre ( 135 155 -5 )^2+ ( -46 93 +6 )^2=47.30 < 8^2 (radius) So, pole inside the circle that

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