Ahoy math friends and welcome to Math Sux! In this post, we are going to learn about the equation of a circle, mainly how to write it when given a circle on a coordinate plane. We’ll see how to find the radius and center from the graphed circle and then see how to transfer that into our equation of a circle. And we’re going to do all of this step by step with the following Regents question. Stay curious and happy calculating! ðŸ™‚

## How do I Answer this Question?

Let’s mark up this coordinate plane and take as much information away from it as possible. When looking at this coordinate plane, we can find the value of the **circle’s center **and the **circle’s radius.**

Now that found the center and radius, we can fit each into our equation:

**Center**=(-3,-4)

**Radius**=5

The only equation that matches our center and radius, is choice (2).

If the above answer makes sense to you, that’s great! If you need a little further explanation, keep going!

## Equation of a Circle:

**Equation of a Circle:** Let’s take a look at our answer and break down what each part means:

So what do you think of circles now? Not to shabby, ehh? ðŸ™‚

Looking for more on circles?Â Check out this post on how to find the Area of a Sector here!

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