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" 3."x^(2)+3x+9=0...

" 3."x^(2)+3x+9=0

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The equation of the circle which touches the circle x^(2)+y^(2)-6x+6y+17=0 externally and to which the lines x^(2)-3xy-3x+9y=0 are normals,is

STATEMENT-1 : Equation of circle which touches the circle x^(2) + y^(2) - 6x +6y + 17 = 0 externally and to which the lines x^(2) - 3xy - 3x + 9y = 0 are normal is x^(2) + y^(2) - 6x - 2y +1 = 0 . STATEMENT-2 : Equation of circle which touches the circle x^(2) + y^(2) -6x + 6y + 17 = 0 internally and to which the line x^(2) - 3xy - 3x + 9y = 0 are normal is x^(2) + y^(2) -6x - 2y -15 = 0 . STATMENT-3 : Equation of circle which is orthogonal to circle x^(2) + y^(2) -6x + 6y + 17 = 0 and have normals along x^(2) -3xy -3x + 9y =0 is x^(2) + y^(2) - 6x -2 y-5 = 0 .

STATEMENT-1 : Equation of circle which touches the circle x^(2) + y^(2) - 6x +6y + 17 = 0 externally and to which the lines x^(2) - 3xy - 3x + 9y = 0 are normal is x^(2) + y^(2) - 6x - 2y +1 = 0 . STATEMENT-2 : Equation of circle which touches the circle x^(2) + y^(2) -6x + 6y + 17 = 0 internally and to which the line x^(2) - 3xy - 3x + 9y = 0 are normal is x^(2) + y^(2) -6x - 2y -15 = 0 . STATMENT-3 : Equation of circle which is orthogonal to circle x^(2) + y^(2) -6x + 6y + 17 = 0 and have normals along x^(2) -3xy -3x + 9y =0 is x^(2) + y^(2) - 6x -2 y-5 = 0 .

Solve by factorization: 9x^(2)-3x-2=0