The standard form of the equation of a circle is given by the formula:
(x – h)² + (y – k)² = r²
In this equation, (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.
To write the equation in standard form, you need to identify the center and the radius. For instance, if you know that the center of the circle is (3, -2) and the radius is 5, you would substitute these values into the standard form:
(x – 3)² + (y + 2)² = 5²
This simplifies to:
(x – 3)² + (y + 2)² = 25
Thus, the equation (x – 3)² + (y + 2)² = 25 is the standard form of the circle with the specified center and radius.