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AP EAMCET201923 Apr 2019Morning ShiftMathematicsCircleActual

The equation of the circle having the common chord of the circles (x^2+y^2-8 x=0 ) and (x^2+y^2-9=0 ) as its diameter is

Options

  1. A(x^2+y^2-72 x-207=0 )
  2. B(x^2+y^2+72 x+207=0 )
  3. C(32 x^2+32 y^2-72 x-207=0 )
  4. D(32 x^2+32 y^2+72 x-207=0 )

Correct answer

C. (32 x^2+32 y^2-72 x-207=0 )

Step-by-step solution

The equation of circle passes through the intersection of circles (x^2+y^2-8 x=0 ) and (x^2+y^2-9=0 is ) ( aligned & (x^2+y^2-8 x )+ (x^2+y^2-9 )=0 & (1+ ) x^2+(1+ ) y^2-8 x-9 =0 & x^2+y^2- 8 1+ x-9 1+ =0 having centre C & ( 4 1+ , 0 ) aligned ) Now, equation of common chord of given circles is (8 x=9 ), and the common chord is the diameter of the circle having centre (C ( 4 1+ , 0 ) ), so ( aligned 32 & =9+9 = 23 9 and (1+ ) & = 32 9 aligned ) ( ) Equation of required circle is ( aligned 32 9 x^2+ 32 9 y^2-8 x-23

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