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Determine the center and radius of the given circle and sketch its graph.$$(x+3)^{2}+(y+2)^{2}=9$$

$$\mathrm{C}(-3,-2) \mathrm{r}=3$$

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

Oregon State University

Idaho State University

Lectures

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In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Determine the center and r…

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Find the center and radius…

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for this problem, we're going to examine the equation. X plus three squared plus why plus two squared equals nine. This is the equation of a circle, and that nine is hard to read. Let me just rewrite that. So it's a little bit clearer thistles the equation of a circle. So in order to do our sketch, we're going tonight. Need to find both the radius and the center of our circle. To do that, let's take a step back and review the standard form for a circle. The standard form of a circle equation looks like this x minus h squared. Plus why minus k squared equals R squared. So on the right hand side, this CO of of this constant is the radius squared. So I just have to take the square root to get the Radius H and K. Give me my CenterPoint. Now it's important to remember that I'm subtracting H and K, so it's X minus H y minus K. That gives me my center points. How do we apply that toe What we've been given in our equation for this exercise? Well, first, let's look at our constant on the right hand side it's nine. So my radius squared is nine. Take the square root that gives me a radius of three. Next, what? Um, I subtracting from X and y Well, you could say that I'm not. It's a plus in both cases, but we can mentally rewrite this. X plus three is like X minus negative. Three. Why? Plus two. Why minus negative, too. So my center is going to be negative. Three. Negative, too. Another way to think about it is that the sign and the equation is always going to be opposite the sign of the coordinates for the center. So it's X plus three. The coordinates. Negative. Three. Why plus to the coordinates. Negative, too. So let's go ahead and graft this. I have the point. Negative three. Negative, too. And with a radius of three, I could just go out and mark three units in each direction and then connect my dots trying to make it smooth. It's it's a sketch. It's not perfect, but close enough to show you that this is indeed a circle. It has a radius of three and a center at negative three. Negative too

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