Final answer:
The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius of the circle.
Step-by-step explanation:
To write the standard form of the equation of a circle, we need to recall the formula. The standard form for the equation of a circle with a center at coordinates (h, k) and a radius of r is (x - h)² + (y - k)² = r². For example, if a circle has its center at (3, 4) and a radius of 5, the equation would be (x - 3)² + (y - 4)² = 25.
To determine which equation refers to the area and which to the circumference of a circle, we must remember that the area is represented by πr² and the circumference by 2πr.