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AP EAMCET202125 Aug 2021Evening ShiftMathematicsCircleActual

If the line x+2 y-5=0 and 3 x-y-1=0 denote two diameters of a circle of radius 5 units, then the equation of the circle is

Options

  1. Ax^2+y^2-2 x+4 y-20=0
  2. Bx^2+y^2-2 x-4 y-20=0
  3. Cx^2+y^2+2 x-4 y+20=0
  4. Dx^2+y^2+2 x+4 y+20=0

Correct answer

B. x^2+y^2-2 x-4 y-20=0

Step-by-step solution

Equation of diameters of the circle, x + 2y − 5 = 0 … (i) 3x − y − 1 = 0 … (ii) Since, intersection of lines (i) and (ii) is the centre of the circle. On solving Eqs. (i) and (ii), we get x = 1 and y = 2 Centre =(1,2) and radius =5 Equation of required circle gathered (x-1)^2+(y-2)^2=(5)^2 x^2+y^2-2 x-4 y-20=0 gathered

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