The Origin ( or just "origin")
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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.
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The centre of a circle is simply called the cnetre. The edge may called the perimeter, the circumference or the edge.
if that line segment intersects the centre of the circle it is called a radius.
A line segment drawn through the centre of a circle and having endpoints on the circumference of that circle is called the diameter. Notably, a line segement with one endpoint at the centre of the circle and one anywhere on the circumference of the circle is called the radius, and is exactly half the length of the diameter.
A quarter of a circle, formed by two radii forming a right angle at the centre, is called a quadrant.
the focus, or centre. focus is more widely used