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AP EAMCET2009MathematicsCircle

The diameters of a circle are along 2 x+y-7=0 and x+3 y-11=0 . Then, the equation of this circle, which also passes through (5,7) , is

Options

  1. Ax^2+y^2-4 x-6 y-16=0
  2. Bx^2+y^2-4 x-6 y-20=0
  3. Cx^2+y^2-4 x-6 y-12=0
  4. Dx^2+y^2+4 x+6 y-12=0

Correct answer

C. x^2+y^2-4 x-6 y-12=0

Step-by-step solution

The intersection point of diameter lines is (2,3) which is the centre of circle. Now, radius aligned & = (5-2)^2+(7-3)^2 & = 9+16 =5 aligned Required equation of circle is aligned (x-2)^2+(y-3)^2 & =5^2 x^2+y^2-4 x-6 y-12 & =0 aligned

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