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AP EAMCET2008MathematicsCircle

If the lines 2 x-3 y=5 and 3 x-4 y=7 are two diameters of a circle of radius 7 , then the equation of the circle is

Options

  1. Ax^2+y^2+2 x-4 y-47=0
  2. Bx^2+y^2=49
  3. Cx^2+y^2-2 x+2 y-47=0
  4. Dx^2+y^2=17

Correct answer

C. x^2+y^2-2 x+2 y-47=0

Step-by-step solution

Since, the lines 2 x-3 y=5 and 3 x-4 y=7 are the diameters of a circle. Therefore, the point of intersection is the centre of the circle. On solving the given equations, we get x=1 and y=-1 ie, the centre of the circle. Required equation of circle is aligned & (x-1)^2+(y+1)^2 & =7^2 & x^2+y^2-2 x+2 y+2 & =49 & x^2+y^2-2 x+2 y-47 & =0 aligned

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