# Given the equation 2x^2 + 2y^2 -8x +20y -6 = 0 a) What is the Center C? b) What is the length of the radius r?

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We have given equation as

`2x^2+2y^2-8x+20y-6=0`

Factor out 2 from each term and write expression as

`x^2-4x+y^2+10y-3=0`

`x^2-4x+4+y^2+10y+25=4+25+3`

`(x-2)^2+(y+5)^2=32`

`(x-2)^2+(y+5)^2=(4sqrt(2))^2`

`` Thus

A. Centre =(2,-5)

B. radius= `4sqrt(2)`

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