yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

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.

More Articles

View All
Worked example: divergent geometric series | Series | AP Calculus BC | Khan Academy
So we’ve got this infinite series here, and let’s see. It looks like a geometric series. When you go from this first term to the second term, we are multiplying by -3, and then to go to the next term, we’re going to multiply by -3 again. So it looks like…
Slash and Burn | Live Free or Die
It should go back down. There’s so much green around it. Yeah, got the fire working for us. Looks pretty good up here. God, we just burnt like 400 square feet or some. Wow, this is the art of slashing burn. Whenever we move into a new area to terrace it …
Andy Grammer JUMP Earth Day Performance | ourHOME | National Geographic
What if I jump? What if it works? What if I’m meant, meant to be more than patient, more than patient? I’m biting my tongue, holding my breath. I think it’s time we had a conversation, a real conversation. Here it go! Make a choice, make it loud. Home is…
Saddle points
In the last video, I talked about how if you’re trying to maximize or minimize a multivariable function, you can imagine its graph. In this case, this is just a two-variable function, and we’re looking at its graph. You want to find the spots where the ta…
How To Make Passive Income with $500
What’s up you guys? It’s Graham here. So we’re going to be talking about something that I have not mentioned for a very long time here on YouTube, and it’s a term that either gets people really excited or makes them feel as though they’re about to be invi…
Eliminate | Vocabulary | Khan Academy
What’s up, wordsmiths? This video is about the word eliminate. [Music] It’s a verb. It means to remove or get rid of something. The word comes to us from Latin, and it’s a combination of two parts: “ex,” which means out or away (think exit), and “limit,”…