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AP EAMCET202123 Aug 2021Morning ShiftMathematicsCircleActual

The line a x+b y+c=0 is normal to the circle x^2+y^2+2 g x+2 f y+d=0 if

Options

  1. Aa g+b f+c=0
  2. Ba g+b f-c=0
  3. Ca g-b f+c=0
  4. Da g-b f-c=0

Correct answer

B. a g+b f-c=0

Step-by-step solution

Given, equation of circle is x^2+y^2+2 g x+2 f y+d=0 Its centre will be (-g,-f) . A normal to this circle will always passes through centre Given, equation of line is a x+b y+c=0 If a x+b y+c=0 , then it satisfied (-g,-f) aligned & a(-g)+b(-f)+c & =0 & a g+b f-c & =0 aligned

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