 Let us look at the distance formula. Given two points, p sub 1 and p sub 2, the distance between them is given by the following formula. Now let us see how we derive it. If we have two points, p sub 1 and p sub 2, with coordinates x sub 1, y sub 1, and x sub 2, y sub 2, the distance between them can be seen as the hypotenuse of the following triangle. Consider the line y equals y sub 1, and let us stop right below the point x sub 2. Here we draw the line x equals x sub 2, so that this point here is the point x sub 2, y sub 1. Now this here is a right angle, so we have a right triangle, so all we need to do is apply the Pythagorean theorem. This side is simply the difference of the y-coordinates, and this side, this leg is simply the difference in the x-coordinates. And this is the distance, so applying the Pythagorean theorem, d squared must be equal to the difference of the x-coordinates squared plus the difference of the y-coordinates squared. And we get the formula that we saw at the beginning. Since distance is positive, we only consider the principal square root, and we get the following formula also called the distance formula. Let us apply the distance formula to the equation of a circle centered at the origin. First let us remember that a circle is the set of all points, the circumference, equidistant from a point called the center. The distance from the circumference to the center is called the radius. Now let us consider an arbitrary point on the circumference, and we know that the radius is the distance from the center of the circle, in this case the origin, to an arbitrary point on the circumference. Let us say that this is an arbitrary point of coordinates x, y. We can simply apply the distance formula, this is r, so r is the square root of the distance between this point and the origin. This is x minus 0 squared plus y minus 0 squared, so this is just the square root of x squared plus y squared. Of course, since the distance is positive, we can also look at it this way. That is the equation for a circle centered at the origin. Thank you.