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

2m read

·Nov 11, 2024

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.

Kathryn Minshew at Startup School NY 2014

Interpreting change in exponential models: changing units | High School Math | Khan Academy

View All

Substitution and income effects and the Law of Demand

In other videos, we have already talked about the law of demand, which tells us—and this is probably already somewhat intuitive for you—that if a certain good is currently at a higher price, then the quantity demanded will be quite low. As the price were…

The Puzzle I Was Never Able To Solve

I’m about to show you a puzzle I’ve known about for most of my life, but was never able to solve until last week. When I gave up, I just looked up the answer. I’m not saying this is the hardest puzzle ever created, but it changed the way I look at life. …

You Don't Need Dopamine Detox

If you’re watching this video on your phone, chances are that before I’m done talking, you’ll get a notification, a text from a friend, a like on a recent post you just shared, or a new follower or subscriber. When this happens, do you feel a rush, a sens…

Nanotechnology: A New Frontier

The world is shrinking. There’s a deep and relatively unexplored world beyond what the human eye can see. The microscopic world is truly alien and truly fascinating. I’m delving further than the microscopic scale; I’m going to explore the potentials of wo…

So Much Change, So Little Time | Sea of Hope: America's Underwater Treasures

We are just beginning to understand that loss of grouper and parrot fish has a domino effect, and kills the reef. It’s happening so fast; it doesn’t take an old-timer to remember the good old days. In just my short lifetime of 19 years, I’ve been able to …

15 Signs You are the New Poor

The World Economic Forum said, and this is a direct quote: “By 2030, you will own nothing and you’ll be happy.” There’s a new breed of poor people out there, some by societal design, some by choice. They don’t look poor on the surface, but they are cursed…

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

More Articles