Divide all terms by 100 and so: x^2 + y^2 -1.2x +y -0.39 = 0
Complete the squares for x and y: (x-3/5)^2 + (y+1/2)^2 -9/25 -1/4 -0.39 = 0
Thus it follows: (x-3/5)^2 + (y+1/2)^2 = 1
Therefore the centre of the circle is at (3/5, -1/2) and its radius is 1
The equation describes a circle with its centre at the origin and radius = √13. Each and every point on that circle is a solution.
The centre is (-5, 3)
Note that: (x-a)2+(y-b)2 = radius2 whereas a and b are the coordinates of the circle's centre Equation: x2+y2-4x-2y-4 = 0 Completing the squares: (x-2)2+(y-1)2 = 9 Therefore: centre = (2, 1) and radius = 3
Equation: x^2 +y^2 -4x -6y -3 = 0 Completing the squares: (x-2)^2 +(y-3)^2 -4 -9 -3 = 0 So: (x-2)^2 +(y-3) = 16 Therefore the centre of the circle is at (2, 3) and its radius is 4
Circle equation: x^2 +y^2 -8x +4y = 30 Tangent line equation: y = x+4 Centre of circle: (4, -2) Slope of radius: -1 Radius equation: y--2 = -1(x-4) => y = -x+2 Note that this proves that tangent of a circle is always at right angles to its radius
The equation for a circle of radius r and centre (h, k) is: (x - h)² + (y - k)² = r² If the centre is the origin, the centre point is (0, 0), thus h = k = 0, and this becomes: x² + y² = r²
The equation describes a circle with its centre at the origin and radius = √13. Each and every point on that circle is a solution.
The centre is (-5, 3)
Note that: (x-a)2+(y-b)2 = radius2 whereas a and b are the coordinates of the circle's centre Equation: x2+y2-4x-2y-4 = 0 Completing the squares: (x-2)2+(y-1)2 = 9 Therefore: centre = (2, 1) and radius = 3
Equation: x^2 +y^2 -4x -6y -3 = 0 Completing the squares: (x-2)^2 +(y-3)^2 -4 -9 -3 = 0 So: (x-2)^2 +(y-3) = 16 Therefore the centre of the circle is at (2, 3) and its radius is 4
Equation: x^2 +y^2 -4x -6y -3 = 0 Completing the squares: (x-2)^2 + (y-3)^2 -4 -9 -3 = 0 So: (x-2)^2 +(y-3)^2 = 16 Therefore the centre of the circle is at (2, 3) and its radius is 4
Circle equation: x^2 +y^2 -8x +4y = 30 Tangent line equation: y = x+4 Centre of circle: (4, -2) Slope of radius: -1 Radius equation: y--2 = -1(x-4) => y = -x+2 Note that this proves that tangent of a circle is always at right angles to its radius
A unit circle is a circle of radius 1. If it's center is at the origin of an xy-coordinate system, then the equation is x (squared) + y (squared) = 1
Equation of the circle: 4x^2 +4y^2 -20x +8y +9 = 0 Divide all terms by 4: x^2 +y^2 -5x +2y +2.25 = 0 Completing the squares: (x-2.25)^2 +(y+1)^2 = 5 Centre of circle: (2.25, -1) Radius of circle: square root of 5
General formula for a circle is X squared + Y squared = radius squared. So the answer would be x squared + y squared = 2.64575131 squared
The centre is (a, a) and the radius is a*sqrt(2).
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