2014-08-06T14:38:21-04:00
Equation of a circles is given as
(x - xc )²  + ( y - yc )²  =  r²
center is (xc, yc)   radius is r  origin is (0,0)
since center is at the origin  xc = 0  yc = 0
circle is x² + y² = r²
radius of the circle is the distance between the point (4, 1) and (0,0) origin.
distance is    √ [ (4-0)² + (1-0)²  ]    = √17
equation is  x² + y² = 17

2014-08-06T14:41:26-04:00
Center of the circle is at the point (0, 0).
Circle passes through (4,1), so radius is r:
a=4, b = 1

Equation of circle:
(canonical form)
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