Graphing circles from features | Mathematics II | High School Math | Khan Academy

We're asked to graph the circle which is centered at (3, -2) and has a radius of five units. I got this exercise off of the Con 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 the center. It has to have a radius of five. The way it's drawn right now, it has a radius of one. The distance between the center and the actual circle—the points that define the circle—right now it's one. I need to make this radius equal to five.

So, let's see if I take that. So now the radius is equal to two, three, four, and five. There you go, centered at (3, -2), radius of five. Notice, go from the center to the actual circle; it's five, 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. So, 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, and it has the point (0, 4) on it.

So, X is 0, Y is 4. So 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).

So I’m not there quite yet. There you go, I am now including the point (0, 4). And 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—that this is (4, 1) and we see that (1, 1) is actually on the circle.

So the distance here is—you go four and another one, it's five. So this has a radius of five. But either way, we did what they asked us to do.