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Determine the center and radius of the given circle and sketch its graph.$$(x-4)^{2}+(y-2)^{2}=9$$

$$\mathrm{C}(4,2) \mathrm{r}=3$$

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

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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for this problem. We're going to examine this equation for a Circle X minus four squared Plus why minus two squared equals nine. We're going to find the center of this circle, its radius, and we're going to sketch the circle now. In order to do that, it's important to remember what the standard form of a circle is. We typically write a circle in this format X minus h squared, plus why minus k squared equals R squared. So this constant on the right hand side is the radius squared and the center of the circle is going to be at the point H k h and care what I'm subtracting from X and y before I square them. So let's look at our circle. The constant is nine. That's our radius squared. So our radius is going to be three units and what I'm subtracting from X and y gives me my center at the 0.42 So if I graph this, there's the 0.42 and I'm going to go three units in every direction. I'm just gonna kind of put those points out there and connect the dots. Okay, so I know it's a little bit more of an oval and pointing in some spots. But approximately that's the sketch of our circle, with the center at the 0.42 and a radius of three.

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