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Determine the center and radius of the given circle and sketch its graph.$$x^{2}+y^{2}+8 x-6 y+9=0$$

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

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

McMaster University

Baylor University

Idaho State University

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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Determine the center and r…

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Find the center and radius…

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Give the center and radius…

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for this problem, we will be examining this equation X squared plus y squared plus eight x minus six y plus nine equals zero. This is the equation of a circle. So in order to sketch this, I'm going to need to find both the radius and the center. Now, if this is given in standard form, it's very nice. Standard form allows us to visually pull out the center and the radius. So let's review what standard form looks like. I'm just going to write this toward the bottom of the screen here. Standard form of a circle X minus, h squared. Plus why minus k squared equals R squared. So, as you can see, I can pull the radius from the constant term to take that square root. And my center is the point. HK, H and K are the numbers of subtracting from X and Y, so standard form is excellent to be able to immediately graph a circle. Unfortunately, what we have been given is not standard form. It is general form. In the general form, everything is on. All the terms were on the left hand side and we set it equal to zero. So Let's change it. Let's go from the general form to the standard form that's gonna require us to complete the square once for the exes. So I'm gonna pull my ex terms together and once for the wise. So I'm going to pull my Y terms together. That nine that constant. I'm going to move over to the right hand side, where it becomes a negative nine. Okay, let's complete the square as a reminder. When we go to complete the square, I'm gonna look at the X term. I'm going to take half of the coefficient in this case four, and I'm going to square it. That's the missing constant. And I can add 16 as long as I do it to both sides. So my first term becomes X Plus four squared now for my wife's the same approach. I look at my y term. I take half of that in this case. Negative three. I square it. So I'm adding nine. And as long as I add nine to both sides, I'm allowed to do that. So that gives me why minus three squared and on the right hand side, I end up with 16. So there's my standard form. I can see from this that my radius well, radius squared is 16. So my radius is four. What a my subtracting from X and y well X plus four. That means I'm subtracting a negative for why, minus three, that coordinate is three. So there's my the information I need to grab my circle. My center is that 123412 negative, 43 There is my point with the radius of four. I'm just going to make marks four units out along each of the cardinal directions and then just connect my dots. It's a little bit lumpy, but it's a good sketch, especially for being on a white board. That is the sketch of a circle with a center at negative for three in a radius of four.

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