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Graphing circles from features

How to graph a circle given the center and either the radius or another point on the circle.

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Video transcript

- [Voiceover] We're asked to graph the circle which is centered at 3, -2 and has a radius of 5 units. I got this exercise off of the Khan Academy graph a circle according to its features exercise. It's a pretty neat little widget here, because what I can do is I can take this dot and I can move it around to redefine the center of the circle so it's centered at 3, -2. So, X is 3 and Y is -2, so that's its center. It has to have a radius of 5. The way it's drawn right now it has a radius of 1. The distance between the center and the actual circle, the points that define the circle, right now it's 1. I need to make this radius equal to 5. If I take that, so now the radius is equal to 2, 3, 4 and 5. There you go. Centered at 3, -2, radius of 5. Notice you go from the center to the actual circle it's 5 no matter where you go. Let's do one more of these. Graph the circle which is centered at -4, 1 and which has the point 0, 4 on it. Once again, let's drag the center, so it's going to be -4, X is -4. Y is 1, so that's the center. It has the point 0, 4 on it. X is 0, Y is 4. I have to drag, I have to increase the radius of the circle. Let's see, whoops, nope, I want to make sure I don't change the center. I want to increase the radius of the circle until it includes this point right over here, 0,4. I'm not there quite yet, there you go. I'm now including the point 0, 4. If we're curious what the radius is, we could just go along the X axis. X = -4 is the X coordinate for the center and we see that this point ... This is -4,1 and we see that 1,1 is actually on the circle. The distance here is you go 4 then another 1, it's 5. This has a radius of 5. But either way, we did what they asked us to do.