If: x^2+y^2 -4x -2y -4 = 0
Then by completing the squares of x and y: (x-2)^2+(y-1)^2 = 9
Therefore the centre of the circle is at (2, 1) and its radius is 3 units
The centre is (a, a) and the radius is a*sqrt(2).
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
If: x^2+y^2 = 12x-10y-12 Then: x^2+y^2-12x+10y = -12 Completing the squares: (x-6)^2+(y+5)^2 -36-25 = -12 So: (x-6)^2+(y+5)^2 = 49 Therefore the centre of the circle is at (6, -5) and its radius is 7
The centre is (a, a) and the radius is a*sqrt(2).
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)
It is the Cartesian equation of an ellipse.
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
If: x^2+y^2 = 12x-10y-12 Then: x^2+y^2-12x+10y = -12 Completing the squares: (x-6)^2+(y+5)^2 -36-25 = -12 So: (x-6)^2+(y+5)^2 = 49 Therefore the centre of the circle is at (6, -5) and its radius is 7
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
x2+y2-4x-6y-3 = 0 Using the appropriate formula it works out as:- Centre of circle: (2, 3) Radius of circle: 4.
Points of intersection work out as: (3, 4) and (-1, -2)
area equals pi r squared therefor r squared equals area over pi. Now find square root of r squared and you have "R" (radius) = 2.821
Pi (3.14) times the radius of a circle squared, equals the circumference of a circle.
Equations: y = x+4 and x^2 +y^2 -8x +4y = 30 The given equations will finally form a quadratic equation such as: x^2 +2x +1 = 0 Discriminant: 2^2 -4*(1*1) = 0 meaning there are equal roots Because the discriminant has equal roots the line is a tangent to the circle In fact the line makes contact with the circle at (-1, 3) on the Cartesian plane