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

1 Answer
Roy E.
Jan 27, 2017

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).

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