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AP EAMCET202018 Sep 2020Morning ShiftMathematicsCircleActual

The equation of the smallest circle passing through the intersection of the line (x+y=1 ) and the circle (x^2+y^2=9 ) is

Options

  1. A(x^2+y^2-9-(x+y+1)=0 )
  2. B(x^2+y^2-9-(x+y-1)=0 )
  3. C(x^2+y^2-9-x+y-1=0 )
  4. D(x^2+y^2-9+x+y-1=0 )

Correct answer

B. (x^2+y^2-9-(x+y-1)=0 )

Step-by-step solution

The family of circles passes through the intersection of circles (x^2+y^2=9 ) and line (x+y=1 ) is ( aligned & (x^2+y^2-9 )+ (x+y-1)=0 & x^2+y^2+ x+ y-( +9)=0 having centre & (- 2 ,- 2 ) aligned ) For the smallest circle, the line (x+y=1 ) must be diameter of the circle, so (- 2 - 2 =1 =-1 ) So, equation of the required circle is (x^2+y^2-x-y-8=0 ) or, ( (x^2+y^2-9 )-(x+y-1)=0 )

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