Factor completely x^3-8x^2-2x+16=
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(x - 4 )² + ( y - 2 )² = 5 → d
the equation of a circle in standard form is
(x - a )² + ( y - b)² = r²
where (a , b) are the coordinates of the centre and r is the radius
the centre is at the midpoint of the endpoints of the diameter and the radius is the distance from the centre to either of the 2 endpoints of the diameter.
to find the centre use the midpoint formula
(a , b) = [ (6 + 2) ,
(3 + 1 )] = (4 , 2)
to find r use the distance formula with points (4 , 2) and (6 ,3 )
r = √(6 - 4)² + ( 3 - 2)² = √( 4 + 1 ) = √5 ⇒ r² = 5
(x - 4)² + (y - 2)² = 5 is the equation
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