How Can I Find the Centre Point of a Circle with Given Coordinates and Radius?

  • Thread starter bikermart
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In summary, to calculate the coordinates of the centre point of a curve given the x,y coordinates of two points and the radius, one can use the general equation for a circle in Cartesian coordinates. This will result in two simultaneous equations, which may require some work but are not overly complicated. Alternatively, one can search for a specific formula that uses x1, y1, x2, y2, and r to directly calculate the coordinates of the centre point.
  • #1
bikermart
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given the x,y coordinates of two points and the radius of a curve. has anyone got a formula for calculating the coordinates of the centre point please
 
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Welcome to Physics Forums.
bikermart said:
given the x,y coordinates of two points and the radius of a curve. has anyone got a formula for calculating the coordinates of the centre point please
One can simply use the general equation for a circle in Cartesian coordinates.
 
  • #3
which is ?
 
  • #5
thats great thanks but that give me two simultaneous equations to work out.
i might be being lazy here but has anyone trawled out the formula such that given x1,y1,x2,y2 and r then a= and b= so i can just stick them in my program.
cheers.
 
  • #6
bikermart said:
thats great thanks but that give me two simultaneous equations to work out.
Indeed it does. But they are not difficult.
 

1. What is the definition of the centre of a circle?

The centre of a circle is the point that is equidistant from all points on the circumference of the circle.

2. How do you find the centre of a circle using algebra?

To find the centre of a circle using algebra, you need to know the coordinates of three points on the circle. You can then use the midpoint formula to find the average of the x and y coordinates, which will give you the coordinates of the centre.

3. Can you find the centre of a circle if you only know the radius?

Yes, you can find the centre of a circle if you only know the radius. To do this, you can use the Pythagorean theorem to find the distance from the centre to any point on the circle. By repeating this process with two different points, you can find the coordinates of the centre.

4. Is it possible to find the centre of a circle if only given a graph or image?

Yes, it is possible to find the centre of a circle if only given a graph or image. To do this, you can draw two perpendicular lines on the circle and find where they intersect. The point of intersection will be the centre of the circle.

5. Can you use the distance formula to find the centre of a circle?

Yes, you can use the distance formula to find the centre of a circle. By finding the distance from three different points on the circle to the unknown centre point, you can set up a system of equations to solve for the coordinates of the centre.

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