the circle's radius is 3 units
the point (- 2, 1 ) lies on the circle
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 radius is the distance from the centre to the point (1, 4 ) on the circle
using (1, 4) and (1,1) in the distance formula, then
r = √(1 - 1 )² + (1 - 4)² = √(0 + 9) =√9 = 3 ⇒ r² = 9
(x - 1 )² + (y - 1 )² = 9 ← equation of circle
substitute the given points into the equation and if equation is true then they lie on the circle
(- 2, 1 ) : (- 2 - 1 )² + (1 - 1 )² = 9 + 0 = 9 ← true
Hence (- 2, 1 ) lies on the circle
(3, 3 ) : (3 - 1 )² + (3 - 1 )² = 4 + 4 = 8 ≠ 9
(3, 3 ) does not lie on the circle
