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AP EAMCET202123 Aug 2021Morning ShiftMathematicsCircleActual

If (4,7) and (-2,-1) are ends of a diameter of a circle which intersects X -axis at A and B , then A B is equal to

Options

  1. A5
  2. B6
  3. C7
  4. D8

Correct answer

D. 8

Step-by-step solution

End points of diameter are (4,7) and (-2,-1) . Then, equation of circle is aligned & (x-4)(x+2)+(y-7)(y+1)=0 & x^2+y^2-2 x-6 y-15=0 aligned General equation of circle is x^2+y^2+2 g x+2 f y+c=0 Compare Eqs. (i) and (ii), we obtain g=-1, f=-3, c=-15 Now, X -intercept is given as, aligned A B & =2 g^2-c =2 1-(-15) =2 16 =8 A B & =8 aligned

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