Question

How do you identify the center and radius of the circle `x^2+y^2=1`?

Answer 1

Center is `(0,0)` and radius is `1`.

Explanation:

It's already in standard form:
`(x-f)^2+(y-g)^2=r^2` is the equation for a circle center `(f,g)`, radius `r`, with `f=g=0` and `r=1`.

Also the equation is asking for the set of all points such that the distance from the origin is `1`. The distance from the origin of point P `(x,y)` is `sqrt(x^2+y^2)` (by Pythagoras's Theorem applied to any triangle) OPN where O is the origin and N is the foot of the perpendicular from P to either axis).