Find all possible equations for circles on the unit circle

The equation of a unit circle is:

$x^2 + y^2 = 1$

Any circle equation that lies on the unit circle must satisfy this equation. Therefore, an example of such an equation is:

$x^2 + y^2 = 1$

which indicates the circle with radius 1 centered at the origin.

Given the standard form of a circle’s equation:

$ (x-h)^2 + (y-k)^2 = r^2 $

For a unit circle centered at the origin, this simplifies to:

$ x^2 + y^2 = 1 $

Another way to express it could be:

$ (x-0)^2 + (y-0)^2 = 1 $

This confirms that the center is at (0, 0) and the radius is 1.

The general equation for a unit circle is:

$ x^2 + y^2 = 1 $

This can be rewritten in the form:

$ (x-0)^2 + (y-0)^2 = 1 $

showing a center at (0, 0) and a radius of 1.

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