Make the equation of a circle centered at point O and radius R = 5.

To draw up the equation of a circle centered at point O with coordinates O (0; 6) and a radius that is 5 cm, we first of all recall the general formula for a circle.

So, this formula can be written as:

(x – a) ^ 2 + (y – b) ^ 2 = R ^ 2;

Where the center of the circle is O (a; b) and the radius of the circle is R.

We just have to substitute the given values into the general formula and we will get the equations of our circle.

So, we substitute and get:

(x – 0) ^ 2 + (y – 6) ^ 2 = 5 ^ 2;

x ^ 2 + (y – 6) ^ 2 = 25.

Answer: x ^ 2 + (y – 6) ^ 2 = 25.