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General equation of a circle: x^2 +2gx +y^2 +2fy +c = 0

Points: (6, 3) (-5, 2) (7, 2)

Substitute the points into the general equation to form simultaneous equations:-

!2g+6f+c = -45

-10g+4f+c = -29

14g+4f+c = -53

Solving the above simultaneous equations: g = -1, f = 3 and c = -51

Therefore: x^2 -2x +y^2 +6y -51 = 0

Completing the squares of x and y: (x-1)^2 + (y+3)^2 -1-9-51 = 0

So it follows: (x-1)^2 + (y+3)^2 = 61

Centre of the circle is at (1, -3) and its radius is the square root of 61

Q: What is the centre and its radius of a circle that passes through the points of 6 3 and -5 2 and 7 2 on the Cartesian plane showing all work from start to finish?

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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.

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.

The equation of the circle works out as: (x+2)^2 + (y-5)^2 = 41 The circle's centre is at: (-2, 5) Its radius is the square root of 41

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.

It is the diameter of the circle.

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It works out that the circle's centre is at (3, -2) and its radius is 5 on the Cartesian plane.

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.

Centre of the circle is at (7, 7) and its Cartesian equation is (x-7)^2 + (y-7)^2 = 49

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.

The equation of the circle works out as: (x+2)^2 + (y-5)^2 = 41 The circle's centre is at: (-2, 5) Its radius is the square root of 41

The points will form a right angle triangle in a circle whose hypotenuse is its diameterLength from (8, 5) to (5, 1) = 5Midpoint: (6.5, 3) which is the centre of the circleRadius: 2.5Equation of the circle: (x-6.5)^2+(y-3)^2 = 6.25

It has centre (0, 0) and radius 5.

Centre of the circle: (3, 8) Radius of the circle: 2 Cartesian equation of the circle: (x-3)^2 + (y-8)^2 = 4

The Origin ( or just "origin") * * * * * That is not generally true. The general formula for a circle, in the Cartesian plane, is of the form (x-a)2 + (y-b)2 = r2 where the coordinates of the centre are (a,b) and the radius is r. It is only if both a and b are 0 that the centre is the origin.

Endpoints: (2, 2) and (10, -4) Midpoint: (6, -1) which is the centre of the circle Distance from (6, -1) to (2, 2) or (10, -4) = 5 which is the radius of the circle Therefore equation of the circle: (x-6)^2 + (y+1)^2 = 25

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