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The equation of the circle which passes through the points (1,0),(0,-6) and (3,4) is

Options

  1. A4 x²+4 y²+142 x+47 y+140=0
  2. B4 x²+4 y²-142 x-47 y+138=0
  3. C4 x²+4 y²-142 x+47 y+138=0
  4. D4 x²+4 y²+150 x-49 y+138=0

Correct answer

C. 4 x²+4 y²-142 x+47 y+138=0

Step-by-step solution

Let A =(1,0), B =(0,-6), C =(3,4) Equation of AB is L : y -0 -6-0 = x -1 0-1 y -6 = x-1 -1 y=6 x-6 6 x-y-6=0 . Equation of circle (c) with AB as diameter is ( x -1)( x -0)+(y-0)(y+6)=0 x²-x+y²+6 y=0 . The system of circle passing through the intersection of the circle C and the line L is given by C + kL =0 x²-x+y²+6 y+k(6 x-y-6)=0 This circle is passing through (3,4) . (3)²-3+(4)²+6(4)+ k [6(3)-4-6]=0 9-3+16+24+ k (18-10)=0 46+8 k =0 8 k =-46 k = -46 8 = -23 4 Equation of circle is x²-x+y²+6 y+ ( -23 4 )(6 x-y-6)=0

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