The properties of a circle help us understand how to write its equation on a graph.

A circle's standard equation comes from knowing its center and how far it stretches out, which is called the radius.

Important Parts:

• Center: This is shown as $(h, k)$
• Radius: This is shown as $r$

How to Write the Equation:

The standard equation looks like this:

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

Example:

Let's say we have a circle with its center at $(2, -3)$ and a radius of $5$. The equation for this circle would be:

$$(x - 2)^2 + (y + 3)^2 = 25$$

When you understand these parts, it makes it easier to draw and study circles!