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AP EAMCET20225 Jul 2022Evening ShiftMathematicsCircleActual

The circle touching the coordinate axes with its centre lying on x-2 y-3=0 is

Options

  1. Ax^2+y^2-2 x+2 y+1=0
  2. Bx^2+y^2+2 x-2 y+1=0
  3. Cx^2+y^2+6 x+6 y-9=0
  4. Dx^2+y^2-6 x-6 y+9=0

Correct answer

A. x^2+y^2-2 x+2 y+1=0

Step-by-step solution

The circle touches the co-ordinate axes and distance of circle (radius) from axes is same If centre is (a, b) and radius r aligned & |a|=|b|=r & (x-a)^2+(y-b)^2=r^2 & (a, b) satisfies x-2 y-3=0 aligned aligned & a-2 b-3=0 & a=2 b+3 & (x-2 b-3)^2+(y-b)^2=r^2 & |b|=r r^2=b^2 & (x-2 b-3)^2+(y-b)^2=b^2 aligned circle pass through (0, b) aligned & (0-2 b-3)^2+(b-b)^2=b^2 & (2 b+3)^2=b^2 & 2 b+3= b & b=-3 and b=-1 & a=2 b+3 & a=-3 and a=1 aligned for (a, b) (1,-1) Equation of circle is x^2+y^2-2 x+2 y+1=0

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