Name: Radius and center for a circle equation in standard form | Algebra II | Khan Academy
Uploaded: 2016-02-21T08:52:05.000Z
Duration: 3 min 51 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

squared plus y minus 4 squared is equal to 49.

What are its center h, k and its radius r?

So let's just remind ourselves what a circle is.

You have some point, let's call that h, k.

So let's say that this distance right over here

is r, and so we want all of the set of points that are exactly

So all the points x comma y that are exactly r way.

And so you could imagine you could rotate around

and all of these points are going to be exactly r away.

And I'm going to try my best to draw at least a

I won't be able to do a perfect job of it, but you get a sense.

All of these are exactly r away, at least

So how do we find an equation in terms of r and h, k, and x

Well, we know how to find the distance between two

In fact, it comes straight out of the Pythagorean theorem.

If we were to draw a vertical line right over here, that

essentially is the change in the vertical axis between these two

points, up here, we're at y, here we're k,

so this distance is going to be y minus k.

We can do the exact same thing on the horizontal axis.

This x-coordinate is x while this x-coordinate is h.

So this is going to be x minus h is this distance.

And this is a right triangle, because by definition, we're

saying, hey, we're measuring vertical distance here.

We're measuring horizontal distance here,

we know that this squared plus this squared must

and this is where the distance formula comes from.

So we know that x minus h squared plus y minus k squared

this describes any x and y that satisfies

Now, with that out of the way, let's go answer their question.

The equation of the circle is this thing.

And this looks awfully close to what we just wrote,

Remember, it has to be in the form x minus h, y minus k.

So let's write it a little bit differently.

write that as x minus negative 3 squared.

is equal to, instead of 49, we can just call that 7 squared.

to do that in the red color-- that our h is negative 3,

and that our k is positive 4, and that our r is 7.

So we could say h comma k is equal to negative 3 comma

Make sure to get-- you know you might say,

You might say, hey, maybe h is a positive 3,

So you'd say minus negative 3, and similarly, the radius is 7.

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Radius and center for a circle equation in standard form | Algebra II | Khan Academy

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