Question

find the center and radius of the circle
2x^2+2y^2-2x+8y=1/2

Answer 1

lets start by completing the squares.
2y^2 +8y = 2(y^2+4y) = 2(y^2+4y+4)-8 = 2(y+2)^2 -8

Answer 2

2x^2-2x = 2(x^2-x) = 2(x^2-x+1/4) -1/2 = 2(x-1/2)^2 -1/2

Answer 3

so your expression then becomes
2(y+2)^2 +2(x-1/2)^2 -8 =1
(y+2)^2+(x-1/2)^2 = 9/2

Answer 4

so the center is (1/2,-2) and the radius is (3/sqrt2)

Answer 5

got it?

Answer 6

ya thanks

Answer 7

great!