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AP EAMCET202124 Aug 2021Morning ShiftMathematicsCircleActual

If two diameters of a circle of circumference 10 lie along the lines 2 x+3 y+1=0 and 3 x-y-4=0 , then the equation of circle is

Options

  1. Ax^2+y^2+2 x-2 y-23=0
  2. Bx^2+y^2-2 x+2 y-23=0
  3. Cx^2+y^2+2 x+2 y-23=0
  4. Dx^2+y^2-2 x-2 y-23=0

Correct answer

B. x^2+y^2-2 x+2 y-23=0

Step-by-step solution

Circumference of circle =10 aligned 2 r & =10 (let r be the radius of circle) r & =5 aligned Now, given that 2 diameters of circle lies along 2 x+3 y+1=0 and 3 x-y-4=0 Centre is point of intersection of diameters gathered 2 x+3 y+1=0 ...(i) 3 x-y-4=0 y=3 x-4 gathered Put y=3 x-4 is Eq. (i), we get aligned 2 x+3(3 x-4)+1 & =0 2 x+9 x-12+1 & =0 11 x-11=0, x=1, y & =3-4=-1 aligned Center is (1,-1) Now, equation of circle whose centre is (1,-1) and radius is 5 aligned & [Equation of circle-centre (x₁, y₁ ) , radius =r

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