Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle.

5x^2 + 5y^2 + 10x − y = 0

5x^2 + 5y^2 + 10x − y = 0 it is the same of
x^2 + y^2 + 2x −1/5y = 0
and then
(x + 1)^2 - 1+  (y−1/10)^2  -1/100=0
 (x + 1)^2 +  (y −1/10)^2  =(101/100)

the center is C(-1, 1/10), and the radius is R= sqrt(101)/10

Yes the slope to this is -5