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What is the diameter of the circle described by the equation 3x^2−18x=30y−3y^2? Express your answer as a simplified radical.

 Mar 20, 2020
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3x^2−18x=30y−3y^2      re=arrange

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

 Mar 20, 2020

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