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AP EAMCET202018 Sep 2020Morning ShiftMathematicsCircleActual

A circle is drawn touching the (X )-axis, with its centre at the point of reflection of ((m, n) ) on the line (y-x=0 ). Then the equation of the circle is

Options

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

Correct answer

D. (x^2+y^2-2 n x-2 m y+n^2=0 )

Step-by-step solution

The point of reflection of ((m, n) ) on the line (y-x=0 ) is ((n, m) ), so equation of circle having centre ((n, m) ) and let radius (r ) is ((x-n)^2+(y-m)^2=r^2 )...(i) ( ) Circle (i) touches the (X )-axis, so (r=m ) So, equation of required circle is ( aligned (x-n)^2+(y-m)^2 & =m^2 or x^2+y^2-2 n x-2 m y+n^2 & =0 aligned )

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