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Simplify: 1/3(6x^2+15 y^2)(6x^2-15 y^2)...

Simplify: `1/3(6x^2+15 y^2)(6x^2-15 y^2)`

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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 .

Find the centre and radius of each of the circles whose equations are given below: (i) 3x^(2)+3y^(2)-5x-6y+4=0 (ii) 3x^(2)+3y^(2)+6x-12-1=0 (iii) x^(2)+y^(2)+6x+8y-96=0 (iv) 2x^(2)+2y^(2)-4x+6y-3=0 (v) 2x^(2)+2y^(2)-3x+2y-1=0 (vi) x^(2)+y^(2)+2x-4y-4=0 (vii) x^(2)+y^(2)-4x-8y-41=0

Solve: {:(2x + y = 2),(6x - 3y = 20):}