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AP EAMCET202420 May 2024Evening ShiftMathematicsCircleActual

The equation of the circle whose diameter is the common chord of the circles x^2+y^2-6 x-7=0 and x^2+y^2-10 x+16=0 , is

Options

  1. A8 x^2+8 y^2-92 x+197=0
  2. Bx^2+y^2-23 x+197=0
  3. Cx^2+y^2- 23 2 x+ 197 4 =0
  4. D4 x^2+4 y^2-46 x+197=0

Correct answer

A. 8 x^2+8 y^2-92 x+197=0

Step-by-step solution

S₁ x^2+y^2-6 x-7=0 aligned & S ₂ x^2+y^2-10 x+16=0 & ~S ₁- S ₂=4 x-23=0 x= 23 4 y= 135 4 = 3 15 4 aligned Co-ordinates of diameter are ( 23 4 , 3 4 15 ), ( 23 4 , -3 15 4 ) Equation of circle is aligned & (x- 23 4 ) (x- 23 4 )+ (y- 3 15 4 ) (y+ 3 15 4 )=0 & x^2+ 529 16 - 23 x 2 +y^2- 135 16 =0 & 8 x^2+8 y^2-92 x+197=0 aligned

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