To find the center and radius of a circle from its equation, you start with a special format known as the standard form of the circle's equation.

This looks like this:

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

In this equation:

• $(h, k)$ tells us the center of the circle,
• $r$ is the radius, which is how far the circle reaches from the center.

Here are the Steps to Find the Center and Radius:

1. Look for the Standard Form:
   If the equation isn't in the standard form already, you need to change it. Sometimes, you might see it as $x^2 + y^2 + Dx + Ey + F = 0$.

2. Complete the Square:
   If your equation is in a more complicated format, you’ll need to “complete the square” with the $x$ and $y$ parts. This can be a little hard at first, but it really helps you get to the standard form.

3. Find the Values:

   • The center $(h, k)$ is the point you find from the equation after making it neat.
   • The radius $r$ is just the square root of the number that’s by itself on the right side of the equation.

Example:
Let’s say you have the equation $x^2 + y^2 - 6x + 4y + 9 = 0$.
You would rearrange it and complete the square to find that the center is $(3, -2)$ and the radius is $3$.

Once you understand the steps, it’s really not that hard!