The equation of a circle with centre (x0, y0) and radius r is given by:
(x - x0)² + (y - y0)² = r²
For the circle with centre (-1, -7) and radius 10 this gives:
(x - -1) + (y - -7)² = 10²
→ (x + 1)² + (y + 7)² = 100
This can be expanded and rearranged to give:
x² +2x + y² + 14y - 50 = 0
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.
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.
Equation of a circle centre the origin is: x2 + y2 = radius2 ⇒ radius = √9 = 3.
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
Centre of the circle is at (7, 7) and its Cartesian equation is (x-7)^2 + (y-7)^2 = 49
Centre of the circle: (3, 8) Radius of the circle: 2 Cartesian equation of the circle: (x-3)^2 + (y-8)^2 = 4
It works out that the circle's centre is at (3, -2) and its radius is 5 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
Centre of circle: (3, -5) Distance from (3, -5) to (6, -7) is the square root of 13 which is the radius Equation of the circle: (x-3)^2 + (y+5)^2 = 13
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.
Equation of a circle when its centre is at (0, 0): x^2 + y^2 = radius^2 Equation of a circle when its centre is at (a, b): (x-a)^2 + (y-b)^2 = radius^2
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.
Equation of a circle centre the origin is: x2 + y2 = radius2 ⇒ radius = √9 = 3.
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
A circle centre (0, 0) and radius r has equation x² + y² = r² The circle x² + y² = 36 has: r² = 36 → radius = 6
End points: (10, -4) and (2, 2) Midpoint: (6, -1) which is the centre of the circle Distance from (6, -1) to any of its end points = 5 which is the radius Therefore the Cartesian equation is: (x-6)^2 +(y+1)^2 = 25