General equation of a circle on the Cartesian plane: x^2+y^2+2gx+2fy+c = 0
Points: (2, 2) (1, 1) and (7, -3)
Substitute the above values into the general equation to form simultaneous equations
4g+4f+c = -8
2g+2f+c = -2
14g-6f+c = -58
Solving the simultaneous equations: g = -4, f = 1 and c = 4
Substituting the above values into the general equation: x^2+y^2-8x+2y+4 = 0
Completing the squares: (x-4)^2+(y+1)^2-16-1+4 = 0
So: (x-4)^2+(y+1)^2 = 13
Therefore centre of circle is at (4, -1) and its radius is the square root of 13
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Using the formula of x^2 +2gx +y^2 +2fy +c = 0 it works out that the centre of the circle is at (6.5, 3) and its radius is 2.5 units in length. Alternatively plot the points on the Cartesian plane to find the centre and radius of the circle.
An infinite number, all passing through the centre.
It works out that the centre of the circle is at (4, -3) on the Cartesian plane and its area is 56.549 square cm rounded up to three decimal places.
Points: (5, 0) and (3, 4) and (-5, 0) Equation works out as: x^2+y^2 = 25 Radius: 5 units in length Centre of circle is at the point of origin (0, 0) on the Cartesian plane.
Points: (6, 3) (-5, 2) and (7, 2) Circle's equation works out as: (x-1)^2+(y+3)^2 = 61 Centre of the circle is at: (1, -3) Radius of the circle is the square root of 61 which is about 7.81 to two decimal places