$Find the Equations of Circles on the Unit Circle$

To find the equations of all circles on the unit circle, we start with the general form of a circle’s equation:

$ (x – h)^2 + (y – k)^2 = r^2$

Since we are dealing with the unit circle, the radius r is 1. Thus, the equation simplifies to:

$ (x – h)^2 + (y – k)^2 = 1$

Here, (h, k) represents the center of the circle. Because the unit circle is centered at the origin (0, 0), h and k are both 0. Therefore, the equation of the unit circle is:

$ x^2 + y^2 = 1$

To determine the equation of circles on the unit circle, we start with the general equation:

$ (x – h)^2 + (y – k)^2 = r^2$

For a unit circle, the radius is given as r = 1. Hence, the equation simplifies to:

$ (x – h)^2 + (y – k)^2 = 1$

Considering the unit circle is centered at the origin (0, 0), the center coordinates h and k both equal 0. Therefore, the simplified equation is:

$ x^2 + y^2 = 1$

A circle centered at the origin with radius 1 has the equation:

$ x^2 + y^2 = 1$

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