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

Features of a circle from its graph | Mathematics II | High School Math | Khan Academy


2m read
·Nov 11, 2024

So we have a circle right over here. The first question we'll ask ourselves is: what are the coordinates of the center of that circle? Well, we can eyeball that. We can see it looks like the center is centered on that point right over there. The coordinates of that point, the x-coordinate is -4 and the y-coordinate is -7. So the center of that circle would be the point (-4, -7).

Now, let's say on top of that, someone were to tell us that this point (-5, 9) is also on the circle. So, (-5, 9) is on the circle. Based on this information—the coordinate of the center and a point that sits on the circle—can we figure out the radius? Well, the radius is just the distance between the center of the circle and any point on the circle. In fact, one of the most typical definitions of a circle is all of the points that are the same distance, or that are the radius, away from another point, and that other point would be the center of the circle.

So, how do we find out the distance between these two points? Between these two points? So the length of that orange line, well, we can use the distance formula, which is essentially the Pythagorean theorem. The distance squared—so if the length of that is the distance, we could say the distance squared is going to be equal to our change in x squared. So that right there is our change in x.

I don't have to write really small, but that's our change in x, plus our change in y squared. Our change in y squared. Now, what is our change in x? Our change in x—and you could even eyeball it here—looks like it's one, but let's verify it. We could view this point as the— it doesn't matter which one you view as the start or the end, as long as you're consistent.

So let's see if we view this as the end. We'd say: -5 minus -4. So this would be equal to -1. So when you go from the center to this outer point (-5, 9), you go one back in the x-direction. Now, the actual distance would just be the absolute value of that, but it doesn't matter that this is a negative because we're about to square it, and so that negative sign will go away.

Now what is our change in y? Our change in y—well, if this is the finishing y, -9 minus -7—our initial y is equal to -2. Notice just to go from that y to that y, we go to -2. So actually, we could call the length of that side as the absolute value of our change in y, and we could view this as the absolute value of our change in x. It doesn't really matter because once we square them, the negatives go away.

So our distance squared, or our distance squared—I really could call this the radius squared—is going to be equal to our change in x squared. Well, it's -1 squared, which is just going to be 1 plus our change in y squared. -2 squared is just plus 4. 1 + 4, and so you have your distance squared is equal to 5, or that the distance is equal to the square root of 5.

I could have just called this variable the radius, so we could say the radius is equal to the square root of 5, and we're done.

More Articles

View All
Changes in equilibrium price and quantity when supply and demand change | Khan Academy
What we’re going to do in this video is think about all of the different ways that a supply curve or demand curve can shift. That’s why we actually have eight versions of the exact same diagram. Each of them is showing where we are right now, let’s say in…
Working at Big Tech Companies Can Be a Trap - Michael Seibel
Hello, my name is Michael Seibel. I’m a CEO and partner at Y Combinator. Before YC, I was co-founder of a company called Justin.tv that later became Twitch and sold to Amazon, and another company called Socialcam which sold to Autodesk. One of the most c…
Designing a Cruise Ship | Making the Disney Wish | Mini Episode 3
The ship needs to be all about enchantment. We take you into a world where the design idea of Enchantment will bring our shift and the stories that we tell alive. We have over 1.2 million square feet of spaces. If you have chopped the ship up and you laid…
Creating a Zombie Soap Opera | StarTalk
What I did is I made it a super. I was like, what if people kiss while zombies are trying to eat them? And then people were like, I like this romance stuff. Relationships, really? Yeah, I mean, I don’t know. I’m interested in that kind of stuff. I mean, I…
15 Steps To Force Your Way Out Of Poverty
Poor people work just as hard, if not harder, than those born into wealth. However, that hard work rarely translates into wealth because poverty, as a system, is designed for survival, not growth. You have just enough to get by until tomorrow but never en…
Ireland’s Underwater World | National Geographic
[Music] [Applause] [Music] The first time I saw it, I just thought, “Oh, how my father would have loved this.” Growing up, I was mesmerized by Cousteau films from the underwater world, and I thought, “Well, that couldn’t be Ireland; that must be some exot…