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AP EAMCET201822 Apr 2018Morning ShiftMathematicsCircleActual

The equation of a circle touching the coordinate axes and the line 3 x-4 y=12 is

Options

  1. Ax^2+y^2+6 x+6 y+9=0
  2. Bx^2+y^2+6 x+6 y-9=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

C. x^2+y^2-6 x-6 y+9=0

Step-by-step solution

Since, circle touches both coordinates axes, then centre will be (h, h) and radius =h aligned & | 3 h-4 h-12 (3)^2+(-4)^2 |=h | -h-12 5 |=h & -h-12= 5 h & -12= 5 h+h & -12=6 h or -12=-4 h & h=-2 or 3 & h=3 aligned Equation of circle will be aligned (x-3)^2+(y-3)^2 & =3^2 x^2-6 x+9+y^2-6 y+9 & =9 x^2+y^2-6 x-6 y+9 & =0 aligned

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