What is the diameter of the circle described by the equation 3x^2−18x=30y−3y^2? Express your answer as a simplified radical.
3x^2 - 18 x + 3y^2-30y = 0 divide through by 3
x^2-6x + y^2-10y = 0* 'complete the sqaure' for x and y
(x-3)^2 +(y-5)^2 = 9 + 25
(x-3)^2 + (y-5)^2 = 34 this is standard form of a circle where r^2 = 34 then r = sqrt34 diameter = 2r = 2 sqrt34