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Determine the center and radius of the given circle and sketch its graph.$$(x-3)^{2}+(y+2)^{2}=25$$

$$\mathrm{C}(3,-2) \mathrm{r}=5$$

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

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Lectures

01:43

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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Find the center and radius…

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Determine the center and r…

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Identify the center and ra…

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for this problem. We're examining the equation. X minus three squared plus why plus two squared equals 25. This is the equation of a circle. So we're gonna want to find the center and radius of our circle, and then we'll be able to do a quick sketch of what the circle looks like. Well, in order to do that, let's take a step back and review the standard form for a circle. Standard form for a circle is X minus h squared. Plus why minus k squared equals R squared. So this constant term on the right hand side is the radius square. So if I know that number, I could take the square root to find the radius. The center is the point HK Agent K, or what I'm subtracting from why. So is one. Think of it as why minus X minus that's going to give us our H and R K. So let's examine our circle. Well, this constant is 25 so 25 is a radius squared square root of that gives me a radius of five. Well, let's take a look at what I'm subtracting from X and y for the X coefficient or the X coordinate of my point. I'm subtracting three. Now I have Y plus two. Mentally, we can think of this as why minus negative, too, Which means the Y coordinate will be negative, too. It's always gonna be the opposite sign. If it's X minus as a positive three, why Plus it gives me a negative, too. So let's plot this on our grid here. Three negative two is right there and with a radius of five. I'm just gonna put going to put some dots, five units all the way around, and I'm just gonna connect those dots. It is not going to be a perfect circle, but it's a sketch, so it's a good approximation. So that's our sketch of our circle with a radius of five and a center at the 50.3. Negative, too.

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