Hey everyone, and welcome back. Let's see if we can give this problem a try. So in this example, we're asked to write an equation for a circle with each of the following characteristics. We're going to start with situation a. Now before I do anything, what I'm going to do is write the standard form for any circle, which is (x - h)² + (y - k)² = r², and this will be how I write the equations once I find what the graph looks like.

Now we're going to start with this first circle here. You can see our center is at (0, 1), so horizontally we're at 0 and vertically we're at 1. I can put h = 0 and k = 1, and that's going to be our center. Now we're also told that our radius is 3. So that means I can go 3 units to the right, 3 units to the left, 3 units up, and 3 units down. And this is going to give us our circle, which is the shape that we're looking for. This is what the graph looks like, and what I also need to do is write the equation. So to find the equation, I can use the standard equation, which is going to be:

x2 + (y-1)2 = 9

Now for our next circle, we're given the center at (1, -2), and this has a radius of 1. So what I can do is go to our graph, horizontally we're going to be at 1, and then vertically we're going to be at -2. That's the center of our circle. I can see that our radius is 1, so I can go 1 unit up, down, left, and right, and this is going to give us the circle we need right here. Now in order to find the equation for this circle, I can use this same standard equation:

(x-1)2 + (y+2)2 = 1

Now for this last situation that we have, we have a center at (-6, 3) for situation c, and then we have our radius as the square root of 5. First, I'm going to find our center on this graph, which is going to be horizontally at -6 and vertically at 3. This one's going to be a little tricky because our radius is the square root of 5, approximately 2.2. So here's how you can draw this circle:

The equation is actually pretty straightforward. So to draw the equation, all you need to do is use the standard equation:

(x+6)2 + (y-3)2 = 5

And that is how you can find the graphs and equations for these circles based on the characteristics that we were given in this problem. I hope you found this video helpful. Thanks for watching.