Hello wonderful mathematics people. I'm Anna Cox from Kella Community College. A circle is the set of all points and a Cartesian coordinate system that are an equal distance called the radius from a fixed point called the center. Let's look at that graphically. If we have a center point, let's call it H K, and every single point on the circle is an equal distance away called the radius. So any point that I choose, let's call this point X, Y, every single point should be this distance away. If we thought about dropping and making a right triangle by dropping a vertical line and a horizontal line, this new point went over the same distance as that XY. So this new point would be called X and we went up the same amount as our center or K. Now, if we use the distance formula, the distance formula says that we are going to subtract the X coordinates here. So this distance here, because it's a horizontal line, is just going to be my X minus my H We don't worry about the YS in that particular case because the YS were the same. If we look at this vertical line, it's going to be the upper Y minus the lower Y, or in this case y -, K and we square them both. So this is really the distance formula. We're finding the distance between two points. Well, it actually is also the formula for a circle. If I square each side and change this D to R for radius, R-squared equals the quantity X -, H ^2 + y -, K ^2, where H K is the center of the circle and R is the radius. Now that's a very important form of a circle, but there's another one that's also important. So the standard form is the one we just looked at, X -, H quantity squared plus y -, K quantity squared equal r ^2. If we took this and used our wonderful algebra skills and foiled it out, we'd get a general form that says X ^2 + y ^2 plus CX plus D y + e = 0. Now eventually with quadratics, we actually put coefficients here. So we'd have AX squared plus B y ^2 plus CX plus DY plus e = 0. And for this second more generic equation to be a circle, a has to equal B. Unit circle means that our radius is 1. So in a unit circle, we have a radius of one and the center is at the origin. So if we have the center at the origin, the origin is the .00 X -0 ^2 + y - 0 ^2 equal 1 ^2. So a unit circle is just X ^2 + y ^2 equal 1. Thank you and have a wonderful day. This is Anna Cox.